Yep, no problem. We've camped in ours several times with those sorts of low temps. I would not even connect the water hose unless it's justs to fill the tank. Use the tank and pump.
Matthew beat me to the master tip. Get yourself a small space heater or two....or three. Just be mindful of your breakers and circuits. In my 31 ft when it's real cold I keep one going in the kitchen, and another very small one in the bathroom...
You're plugging in for electricity, right?
The furnace will burn a lot of LP more worse it's blower will drain the house battery in nothing flat. I use the furnace but a bit sparingly....only to warm the place now and then, turn it off when sleeping, turn it on in the morning to warm the place for the wife and kids. The little heaters keep it decent
Most of the pipes are inside so it shouldn't be an issue....
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