Air source heat pumps also have the problem that their (outdoor) radiators freeze is cold weather, so they have to run an electric heater (outdoors) to keep melting the ice. This lowers their cold weather efficiency even more, I imagine it might even make it negative (You have to put more energy into stopping the radiator freezing then it can extract from the cold air).
I did some more reading on this and it seems that you can avoid this issue on reversable heat pumps (ones that also work as air conditioners) by reversing the flow and using heat inside the house to melt the ice.
So it should always be at least a tiny bit more efficient than resistive electric heating unless its about -20C outside.