Our heat pump does fine down to about -5 F, and doesn’t use any resistive heating elements.
It will produce heat down to -15F, but at those temperatures the house loses heat faster than the heat pump can replenish. If the house had better insulation, it would probably keep up.
But we knew and understood it’s limitations going in, so when it’s very cold we augment with wood heat.
Fortunately -15 is rare where the house is situated, and below 0 only happens a few times, most years.
It costs far less to run than our propane furnace did, and keeps the house more comfortable to boot.