As Desert Captain says, if your motorhome is designed for cold weather operation (with enclosed heated tanks and plumbing runs, rather than them all hanging down underneath in the open) you should have no trouble at all. I've camped more with the overnight temperatures have been in the 20's and had no trouble, and would not expect you to either. The furnace does use propane at a relatively quick rate, so keep an eye on that.
My bigger concern is driving through winter weather, especially as they tend to salt the roads a good bit up in this part of the country. Road salt does a number on vehicle frames, and the angles etc. that the house part of the motorhome is built out of are not especially corrosion-resistant, at least on my unit. Washing it off afterwards if possible is a good idea. (I also prefer not to drive the motorhome on slippery roads, although when I've been stuck with having a drive through snow it behaved decently.)