Temps in Alamogordo are not too bad. We've visited friends there in the winter without significant problems. Also, Elephant Butte area or south, but you might see an occasional snow storm. Not too much and it won't last long. El Paso area also gets cold snaps, but nothing too bad. We've also seen significant snow in Demming, but it didn't last long. Just stay toward the south edge of the state and be aware of your altitude. We've been in Albuquerque in January at 17 degrees with 20-30mph winds coming through Tijeras canyon. Definitely NOT recommended.