That time of year you want to think Southwest, not northern states. Most of Yellowstone is closed during the winter months for good reason.
Utah is my all time favorite place on earth but it also gets down right cold during winter and Arches and the Moab area will get snow. Best time of year for Moab is around March - April and then Sept - Oct.
I agree that NM and AZ are probably best for winter riding - how about Sedona? Still cold but not snowy. And not that it is particularly a mountain bike destination but there is plenty of riding and you can't beat the weather in Southern California especially in December.