Standard air source heat pumps can only be used for heating in temperate climates -- when the outside air temperature gets really cold, the heat exchanger gets covered with ice, which reduces its ability to absorb heat from the air. Ground source heat pumps are only an alternative if you can dig into
the ground -- if your house is build directly on bedrock, it's impossible.
I propose the following alternative for heating one's home using a different kind of air source heat pump.
Start with cold outside air. Compress (with an electric motor) it to such a degree that it becomes "warm." Use a heat exchanger to move that warmth into the home's radiant heat system. Dehumidify the air. Expand that cooled, compressed air, through a thermally insulated air powered motor (using the mechanical energy to reduce the load on the electric motor). Discharge the air to the atmosphere.
Dehumidiying the air is vital, otherwise any moisture in the air could turn to ice when the air expands.
I can think of two ways to do it.
The first one is to use a vortex seperator after cooling, and after each stage of expansion (if multiple stages are used). This would allow liquid water droplets to be removed before they have a chance to freeze, and might also be able to remove some frost/snow. It wouldn't be able to remove 100% of the H2O, so some ice would form through deposition... if it's a small enough amount, it might not be a problem.
The other way I can think of to dehumidify the compressed air would be with a liquid dessicant. This dessicant could be pressurized/pumped into the system (with the aid of a pressure exchanger), sprayed through the compressed air, then depressurized through the pressure exchanger. I'm not sure how much heat would be needed to be regenerate the dessicant, but the heat could probably be provided using a conventional heat pump, using the heat already moved into the house as it's source.