I’m not sure which generator you have but this one looks to run about 5 to 6 hours on a 20 lb tank. Others I’ve looked at seem to have the about the same runtime.
Propane has a freezing point of -44°F so it should work well at 20°F.
I don’t know why you’re experiencing the issues you’re running into but maybe look into the generator side to see if there’s anything that can be checked like the orifice for clogging.