I'm in GA, so we flirt with freezing temps all winter. Like others have said, "maybe" is the correct answer. If we are going down to 28-30 for a couple of hours I don't worry about it, especially if we are in the 70's the day before.
With your camper at the house, running the furnace at 50ish is cheap and easy insurance.
I normally winterize 3-4 times a year since we will have a nice weather mid winter. I've got winterizing down to a 10-15min job, not counting getting the camper from storage, and leveling in my sloped driveway.