I don't know if you two like winter driving or not.

I-80 from Salt Lake to Colorado is challenging in winter from time to time due to weather.

At that time in Yellowstone only the North Gate is open. Only the road from North Entrance to Upper Mammoth Terrace and Mammoth via Tower Junction to the Northeast Entrance is plowed. However, if you like snow, there's plenty to do there at that time. You can do cross-country skiing, snowcat riding, or snowmobile.