In December we're skiing here in Colorado. Even places in UT can be quite cold by that time. For instance we've camped in Moab in late Nov. and late Feb., but between those times, it will be cold. Your rig will have to be winter ready for freezing temps, perhaps days where it stays below freezing all day.
Maybe Zion? Milder climate down there. Or further south. Tucson AZ and Big Bend in TX are much more attractive in late December.
If you really have your heart set on CO, I'd look around the southern Front Range. Maybe Pueblo Reservoir and the like. Or look at just motelling it for this trip. Is your family ready for cold days and nights and very short days at that (the winter solstice is during the last two weeks in Dec.)?