Additionally, for proper efficiency the key components of the system need to be sized for your target temperature and the temperature range of your ambient air.

Don't confuse the two.

The efficiency of a home heat pump declines as the air temperature outside the home drops. A freezer is working in reverse so it's efficiency declines as the air temperature outside the freezer box rises.

Neither a heat pump in an Alaskan winter nor a freezer sitting on a Florida back porch in summer are operating very efficiently.

Now, the original claim of "heat pumps don't work below freezing" is trivially wrong (and so the question by lasson was justified), but the overall point is that heat pump efficiency gets worse the more you need it in the case of keeping your home warm.

Invalid assumption.

Whether it can or not depends on the environment.

Most ordinary freezers are designed to operate within a relatively luxurious temperature controlled in-door environment. Stick one in the sun on a Florida back porch in August and you may well discover it can no longer successfully "extract energy from the side that is below freezing". Same thing (only in reverse) can happen with a home heat pump in an Alaskan winter.

There is another important element here --- energy loss and insulation.

At a certain temperature (whatever it may be), the energy lost to the surroundings will start to exceed the capacity of the heat pump. At some point; speaking in practical terms, the heat pump becomes essentially worthless. You need either a bigger heat pump or you need more insulation to stop the loss --- both of which cost money and can't be obtained/installed immediately.