This says modern heat pumps can work down to 5F or colder, but I don't know if the equipment size can be squeezed down to use in a car.
Yes, they can. They also operate in a static environment. At 20F, the coils on a residential heat pump are just sitting still at 20F. They aren’t moving at 60mph into the cold air or being pummeled by rain or snow, while attempting to produce heat from the cold.
On a residential unit, and I would imagine an automotive unit, two conditions can activate the heat strips. One is ambient temperature, the other is a call for a temperature increase of more than 2F above the current setting. If the house is 66F and the thermostat gets set to 70F, the heat strips will activate, even if it is 50F outside.