ACs are very efficient (more than 100%!). By using an AC to heat (a Delta(T) in my city of at least 30C) your home in the winter you more than offset the carbon to cool and dehumidify it a mere 5-10C (again, in my case).
Heating a home in cold climates are far worse than cooling, but there's a puritan rejection of AC:.
- The Delta(T) is larger to heat a home than to cool it. Delta(T) sets the heat loss through your walls.
- There is an attitude that cooling is hedonistic, while heating is a necessity, but it's thermodynamically and metabolically far easier to heat than to cool.
- Most heating is done with fossil fuel furnaces which are at best 90-95% efficient. A heat pump can be over 300% efficient [1] (i.e. it moves 3J of heat from the cold side to the hot side using only 1J). This is much better improvement in performance than an electrical car.
Get an AC that can work in reverse, and if you want don't use it in the summer.
EDIT (added following):
[1] The metric here is coefficient of performance, COP = Thigh / (Thigh - Tlow). For 30C to 20C the theoretical maximum is 3 000%, or 30x
[2] No, you can't break thermo laws with [1].