It all depends on how its set up. If you have natural gas it is unlikely IMHO a heat pump is worth it since natural gas is cheaper than dirt right now. A heat pump may be more efficient than a natural gas furnace at warmer temps, say above 40, but not necessarily cheaper.
Some heat pumps are set up to lock out under a certain temperature.
Now we Have either electric or propane as our heating choices.
We have a higher efficiency heat pump, It makes sense to run ours to -10F due to the efficiency of the unit, and our use of costly electric heat strips as backup.
So if its over -10f and the thermostat is calling for heat, the outside unit is running. When the unit goes into defrost mode, the outside units fan shuts off and the compressor continues to run. (basically it reverts back to being an air conditioning unit, it will remove heat from the house to warm and defrost the outside coils).
On our unit it will not defrost when the outside temperature is over 50F because it is not needed.
Now the heat strips will kick on when the unit goes into defrost (otherwise you would have cold air blowing out of your registers) OR when the heat pump cannot keep up due to the outside temperature being lower. This is called the balance point.
Our balance point is roughly 25F. Anything lower than that supplemental heat is required. It Depends on the wind, if we have basement registers open ect.
Now you can put your thermostat in "emergency heat" mode. Basically this turns off the outside unit, no matter the conditions, and will strictly run your heat strips in the furnace, or propane/gas burner. This is intended if you have an issue with your outside unit.
Heat from a heat pump is very efficient. You are not burning any fuel to create heat when just the heat pump is running, you are just paying to move the heat indoors.
Like I tell my wife, our heat is free, we just have to pay to get it in the house.