We did this exact thing for an entire winter in Northeast PA. I had a water spigot in the basement of the house so hooked up there. I wrapped a hose in foil then put pipe heat tape and wrapped in pipe insulation. Pretty much a redneck heated hose I guess. Only time anything would freeze was in single digits or less and then I just put a torpedo heater under FW for a little while. I did have skirting that a made up around most of the unit and heat lights in the under belly in a couple of spots.
When renovating my focus was bathroom then kitchen so we basically were sleeping in RV at that point. I also ran a hard sewer line through a basement window for sewer drain.
It can be done, but you will burn through lots of propane. Looking back I should have gotten a 100lb tank instead of cycling through 30 and 40 lbers.