I would not advise Four Corners. Really...there is nothing there but open flat land and especially in winter it would be dismal, windy and cold.
Keep in mind that I-40 from Flagstaff to Albuquerque also is bad in winter. In fact, the interstate was closed down for us one year the end of April. You just never know.
I really would advise renting in Phoenix and go as far north as Sedona and if you're adventurous - on to Grand Canyon. For that you won't want to drive on 89A from Sedona up to Williams. It's steep, curvy and does get snow. Instead, take I-17 north from Sedona but it isn't great either if it snows.
Arizona is all about elevation. If you look on a map of it, the mild winter will be from Phoenix, west to Havasu City, south to Yuma and east to Benson. Don't try for Payson or Show Low. East of Benson will be nothing of interest in winter - flat and open. New Mexico is colder than Arizona, and true in the southern part. It's higher in elevation than Arizona's southern part. Getting up to Santa Fe you'll have snow. There's a ski area there.
We're not trying to discourage your trip but just trying to steer you in the right area during winter. There are plenty of great things to see in southern Arizona.
