Tell me if I'm crazy?

You are not crazy and sounds like a fantastic adventure. There are plenty of private campgrounds that are open year round. We took that trip during Christmas and New Years about 3 years ago. We had a fantastic time. That area is just made for RV's. If you can't find a campground, there are plenty of wide open spaces that you can run the generator and just park overnight to sleep. Keep your water tank full while traveling, as there may be some parks that may not have their water turned on due to the time of year. The campground at Arches is a primitive campground, but absolutely gorgeous. I don't know where these people get their information when they tell you that you need a commercial license for a private motorhome for personal use. This is utter nonsense. You just need a regular driver's license. Have fun and enjoy!