My roof top Dometic AC/heat pump will still put out heat down to 37 degrees. I have heard that some will not work below 40 and some will work down to 32 degrees. I am sure that even two identical AC/heat pumps may not work at the same low temperature.
For your furnace to work, it must have 12 volts available and you must have propane available to the heater. If it is controlled by the same wall thermostat that controls your AC units, the thermostat must have 12 volts available to it.
You need to check all of your 12 volt fuses to insure that they are not blown.