It helps if you can understand the difference between heat and temperature. Heat is the total thermal energy in a system, and temperature is the average thermal energy in a measured sample.

Example. If I have a known quantity of air, I can measure its temperature, and from that information I can determine how much heat is in that air. If I compress that air into half the space, the temperature will go up, but to total heat in the system will stay the same.

Heat flows from high temperature areas to lower temperature areas, and the greater the temperature difference is, the faster if flows. So if you take the air in our example, and put it in a refrigerator, it will eventually cool down to the same temperature as the refrigerator. If you then expand that air back to the original volume, you'll see a drastic reduction in the temperature, but the overall heat won't change.

So if you want to get heat from a colder source, all you need to do is compress that air first, which will raise the temp, move that higher temp air into your house, where it will warm up your house and cool off, then move it outside and let it expand again, where it will fall below the temp of the outside air, and it will warm up again, and you can repeat the cycle.

As long as it above 0K outside, you can (in theory) transfer energy. Heatpumps meant for cold weather climates use a different gas with a lower boiling point than those meant for hot weather climate (aircondition). But other than that, they work exactly the same.

The element can cool the air below zero. They have to play games if it gets to the due point of the outside air to keep from frosting up however.

Also, there is an efficiency hit, as the temperature differential gets larger. This is why ground sourced, or even water sourced are more efficient in colder climates.

Do you understand how an AC unit works when its hot as tits outside? I cant remember the specifics but its air pressure. One way makes it hot, the other makes it cold. Just reverse it for whichever situation you need it to be