Telsa solved that long-standing problem by engineering the new Model Y heat pump design to include a local heating loop. This allows the heat pump to self-prime itself where other heat pumps fail to start the cycle due to cold temps. Once the heat pump is started and operating normally, it then continues to operate more efficiently than a resistive heater, even in cold temps.
Here's
how Elon described the Model Y heat pump on the recent 3rd Row Podcast: (time index 5:18)
"The thing that's really interesting about the heat pump design is that it has a local heating loop. So heat pumps typically encounter issues around -10 to -20 C. They have a problem spooling up. Essentially they can't get going, the cycle can't get going.
"So the solution that the HVAC team came up with was to have a local heating loop. So the thing will basically just sort of spin itself up and get hot locally before opening another valve that then tries to heat the cabin.
"So a heat pump with a local loop. That local loop part is very important for low temperatures and that's where really I think a lot of heat pump designs fail is they don't have a local heating loop"