As inverter air conditioners changes the compressor speed, and therefore, the heating capacity and not always operates at 100% speed, like regular air conditioners, I've wondering: Are inverter air conditioners can heat better at lower outdoor temperatures than regular air conditioners without freezing the outdoor evaporator coil with ice?

The freezing on the outdoor coil will always happen when outdoor temperature goes below 10..5degC, but to handle that the units use defrost cycles, so it is not that much of a problem, neither for the efficiency (as the defrost cycle consumes energy but does not generate any useful heat).
However the major problem at low temperatures is just the relatively low mechanical efficiency of present technologies and the second law of thermodynamics (the need to transfer the heat over larger temperature difference).

The inverter technologies allow to size the units to higher power without that much significant impact on the efficiency at the power levels most frequently required during operation, even at the relatively light load when operating at cold outdoor temperatures.
What remains is the need for more complex refrigerant storage within the unit, as the wired temperature range means the amount of refrigerant required within the system is higher (in order to maintain the power level) and a compressor which is able to handle both higher volumes and higher compression ratio at low pressures (when pumping from cold; so to have high displacement), at other time the system needs to handle higher pressures when temperatures are higher (so less transferred volume). With the inverter technology it becomes easier (allows efficient operation even at low rpm, so allow to maintain the transferred heat power  when the compression ratio is low withot the need for mechanically more complex variable displacement compressor), as said above.
But even variable displacement compressors are not that big problem - these days it is rather common technology in automotive, so I think moving them to house refrigeration won't be that big deal. But they are more complex than the simple crank/piston designs commonly used in fixed refrigeration.

All modern air conditioners (Including regular on/off) here in Israel, now uses only either vane or scroll compressors. Hence they are very silent.
only 90's and earlier air conditioners here used reciprocating compressors which were noisy and can't change speed.

The scroll or vane compressors have one huge disadvantage: They lose efficiency very rapidly once the compression ratio departs from the operating point they are designed for. So they lose efficiency once the temperatures depart from the design optimum. This may become acceptable for air conditioning, but the wide temperature ranges related to high efficiency heat pumps would mean the efficiency would become poor (it always operates at the ratio dictated by the geometry, then just dropping the excess pressure by passing the gas via narrow constriction).
Reciprocating piston (with simple reed valves) can vary the compression ratio in virtually unlimited range, the passive valves are just controlled by the pressure, so the efficiency remains pretty constant over very wide range of compression ratios.
Yes, the losses are a bit higher compare to a scroll or vane type operating at design ratio, but once the pressure requirements are forced to depart from that optimum, the efficiency of the rotary drops very significantly while the reed valve piston remains quite constant.

But the compressor does not have to be rotary (vane or scroll) type in order to be silent, with reciprocating design it is just matter of balancing the thing out.
Frequent way is to use V-90deg two cylinder configutration, a simple counterweight on the motor shaft does balance the pistons near perfect, so the only vibration remains is the torsion one (because of the irregular loading along the rotor position angle). But with an inverter technology this is not that hard to suppress, you just design the synchronous motor so the peak torque from the motor itself matches the phase with the peak torque requirement of the 90deg V-twin compressor arrangement (when both are compressing). It leads even to rather simple single phase BLDC design, sufficing with just a simple 4-transistor bridge as the power stage of the inverter.

Other popular option is a star 3 cylinder configuration, this balances all forces naturally, include majority of the torque vibration (the load is spread evenly over the whole 360deg). But the drawback is more cylinders, so higher piston surface/volume ratio, so it goes mainly towards higher power systems. This then works even with basic induction motors.

By the way car air conditioning compressors are virtually all piston reciprocating type, usually about 5..9 cylinders or cylinder pairs (for double acting designs) and that makes them perfectly smooth.

Yes, multiple cylinders do not work that well for low power systems (like fridges or so; due to high surface-to-volume ratio related losses), but house HVAC uses to operate at power levels where these losses are not that bad.

Linear vibrating compressors are a technology many companies are experimenting with, because of simple linear motion it is rather easy to balance out any forces so they do not transfer any vibration to the case at all at the same time having just one cylinder so very good surface/volume ratio, but it is really in its infancy, far away from getting released "into the wild". So far LG tried it in home refrigerators and it was huge reliability failure.

I thought that car air conditioners uses scroll compressors. And how the modern air conditioners are so quiet if they are using reciprocating compressors?
Video of a local made air conditioning unit from the 90's on heating.
Video of a modern Gree made air conditioning unit, on heating.
I doubt that the newer Gree one have reciprocating compressor, as it is much quieter than the older local made one.

To be quiet, you need to cancel out all vibrating forces. That means making the thing perfectly balanced in all axes.
With rotary it is rather simple - the imbalance is of an excentric nature around the shaft, so a simple counterweight and zou are done.
With a linearly moving single cylinder zou have a problem: The piston assembly is "shaking" only in one axis, the crank is an eccentric imbalance. Now if you add just a simple counterweight, you may balance out either one direction (along the piston movement) or the other (perpendicular to it), but not both. The seemingly best you may do is to balance them so you get an eccentric imbalance again. But there is a problem: It is rotating in the opposite direction towards the shaft. So you would need extra counter rotating balancer shaft. Acceptavble for things like combustion engines, but not for such compressors.

But if you add an extra cylinder perpendicular to the first one, it's inertia will add the extra component on the perpendicular axis, so the total imbalance becomes again an eccentric one and rotating along the crank. So just simple counterweight and you are perfectly balanced again.
But with this what remains is the rotating load on the shaft (when cylinders are compressing) is present at about 120deg of the shaft rotation, the res 240deg there is no load. So we still have a bit of torsion vibration.
But to counter that what is sufficient is to make the compressor core (the motor + compressor assembly within the "egg") mount very light in holding the torsion, so it lets the whole motor assembly mass to counter that torsion vibration and do not propagate them to the case.
Or (and there the inverter technology with a synchronous permanent magnet motor becomes handy) design the motor in a such way so it generates the torque exactly when and how much the compression just needs it, so even the rotation vibration gets compensated.
And then your compressor becomes silent even if reciprocating.

And then other option is to use more cylinders in a regular star pattern around the axis. This has the advantage to cancel out not only the linear imbalanc components and the only what remains is an eccentric rotating along the shaft (so a simple counterweights balance that out), also the major higher order ones coming from the connecting rod arrangement distortion, plus also distributes the rotating load evenly along the shaft rotation, so making it to vibrate less even in the torsion mode. Plus this is easy to isolate from the case.


Of course this works when the cam to piston is done by a sliding mechanism, which yields exact sinewave motion. Using connecting rods (as in common combustion engines) distort it a bit, so there remains some higher harmonic imbalances (on a multiple of the crank rotation speed). But even that, because it becomes in way higher frequency, it becomes easier to "filter it out" by the core assembly mass and the suspension springs, so it could be made still quite smooth.

I believe virtually all mini-split systems use a rotary vane compressor.

@Metal Halide Boy: This is the noise of my hostel Gree A/C at heating: https://www.lighting-gallery.net/gallery/displayimage.php?pos=-222521
Looks either reciprocating or scroll. The compressor sound don't hearing smoothly like that of a rotary vane compressor but more like rugged noise which usually the characteristic of reciprocating compressor, even if it silent.

I believe virtually all mini-split systems use a rotary vane compressor.

Mainly if they are "cooling only", the scroll was indeed one of the most common type of compressors, because it is indeed very easy to make them quiet: All inherent imbalances are 100% pure rotary with the shaft, so simple counterweights 100% cancel them. Plus virtually no torsion vibration, so able to use directly mains fed induction motor (no need for torsion vibration canxcellation).
 But it has fixed compression ratio, so efficient only for a given temperatures, once the temperatures deviate, efficiency drops. That was not that big deal for just cooling air conditionning, the simplicity and mainly cost was the stronger argument.
But once the efficiency at wide temperature ranges becomes the main focus, the reciprocating pistons have quite an edge, mainly when paired with an inverter, so active torsion vibration cancellation is not that difficult, so even machines with strong inherent torsion vibration (single cylinder or V-twins) are able to run completely quiet.
These things make the reciprocating compressors coming back into the HVAC business...

Interesting. Here in the US scrolls have virtually killed off reciprocating compressors, and we have a lot of rotary compressors now as well. Sounds like in other countries reciprocating compressors have remained more common.

I would not be 100% sure all are scrolls.
Definitely the age of loud buzzing monsters is gone by (maybe except some ofthe really cheep models), there is no arguing about that.
But a scroll is not the only way to get that, there are many ways how to reach similar quiet operation.

One possible way is to dynamically balance all moving parts (V-twin, star configuration, reciprocating balancing mass, counterrotating balance shafts,...).

Other ways, mainly popular on low power systems (fridges,...) is the compressor core suspension to be extremely soft in the direction of the vibrations, so it lets the core vibrate inside of the compressor "egg" shell, but do not pass that vibration to the shell. The point is, the only direction the suspension needs to hold any significant forces is the gravity, to support the mass of the core. And usually there is at least one direction, in which there is no vibration at all (along the shaft...; that is why virtually all "sealed egg" compressors use vertical shafts). It is one of the oldest and simplest methods, but given the modern (CAD) design capabilities, it becomes practical to make it so efficient and against vibration modes in a way no one thought to be possible just few years ago. This includes controlling vibration transfer via electrical connection, as well as gas piping (the way how these are shaped/routed within the egg case).

Often resonant traps are used (spring/mass resonators tuned to the vibration frequency, so they hold either the core itself, or part of its suspension steady, so the vibration can not transfer to the case). But I think this method will be more on its decline, as it requires the machine to operate at exact rpm, so good for "tradditional" mains frequency motors, but won't work with variable speed inverters.
 
With innverters feeding the motors, using active vibration compensation/suppression becomes not that difficult to get (mainly for the torsion vibration modes, coming from the uneven load of the motor - modulate the generated torque so it matches the load).

And most often some combination of multiple methods is used, as each is practical/effective only for some modes or only to some extend.