Air-to-air heat pumps struggle when it's below freezing, because there's little heat outside to pump into the house. When it gets really cold, heat pumps use electrical resistance heating wires to keep up with heating demand.

Water-to-air systems would work better in a cold climate, but the efficiency goes down as the heating or cooling season progresses because the ground (closed loop0, ground water (open loop) , or pond water (closed loop) gets heated or cooled. Water-to-air systems are also stupid expensive.

Heating with heat pumps is also uncomfortable. The heated air is warmer than the room temperature but less than body temperature, so if you have a vent blowing on you it feels cold.