You need power to run a propane furnace or most any other space heater, unless you go to wood-fired heating or something like that. Most propane furnaces will run down a typical Class C battery bank over one night, certainly will not do two without recharging. Most Class C alternators can't fully recharge a battery bank without running for 4 - 6 hours. I don't understand no generator, but you will either need more solar than will probably fit on top of your MH or a certain 4 - 6 hours a day on a pole somewhere. If you have no dump stations you have to either not use water inside the MH or create a dump station.
Does not sound like a plan to me.
Brian