It will still work, just not as efficently as in normal temperatures. So you're using 50kWh for the 3 days a year it's that cold and 10kWh for the other 362 - better than using 20kW every day.

Only if there is enough power generation

And a good 24,000 BTU rated heat pump will produce just under 20,000 BTU at -13 F, about 18,000 BTU at -22 F (-30 C).

Fortunately resistive heating is just about the cheapest possible heating in capital costs and trivial to retrofit as a backup.