With the temps you are talking about, your best bet is to dry camp. Tanks will freeze unless you have tank heaters, and even that isn't a solid bet. We used to do it with our popup, use the bath house, no water in the trailer tanks, maybe a cooler of drinking and cooking water.
Using the LP furnace you are going to go through a lot of LP. Easily 20# tank a day, if not more. I used electric heaters and an LP fired Buddy Heater to take some of the load off the main furnace.
Not saying it can't be done, just not easily or cheaply.