Without knowing what sort of RV we're talking about it's hard to say what you can expect. I had one TT that I could only use dry if the temp was going to drop below mid 20's or so. The gate valves for the black and grey tanks were under the trailer and would freeze and crack fairly easy. The exposed water lines would also freeze, but it never caused damage. Other rigs I've owned with heated and covered undercarriages would do much better.
I would definitely want my furnace to work, and would be wary of this trip if you're not familiar with camping in cold conditions. I'm comfortable camping in a snow cave and always have bedding suitable for such when I take my machine out into the weather. Unfortunately, while I can survive, the RV doesn't necessarily adapt so well to the cold all the time. It takes a little more work and experience to get the mechanicals ready for winter.
