During the holidays, typical weather along I-10 in southern Arizona and New Mexico will be mid-60's during the day and around 40 degrees at night. However, it could be up to 75 and down to 20 depending on whatever is blowing through.
We don't winterize, as the typical light frost usually won't bother your pipes or tanks. Also, you'll be staying in your Airstream; so if you hear the evening news warn about a hard freeze and everyone should cover their citrus trees, just make sure to run your furnace and you should be fine. The lowest setting is OK, which is about 50 degrees.
Note: All temps are Fahrenheit.
We usually don't get much rain, nor any snow, during the holidays. However, if there is any precipitation, you might see a light dusting of snow on the mountains. It is very rare to see any ground accumulation of snow, and that won't last more than an hour or two after sunrise. The one exception is Texas Canyon, which is a slight rise between Benson and Wilcox, AZ. However, you don't have to worry about this unless it's actually raining or snowing (or was overnight), and you'll hear any problems on the TV and radio weather reports.
Great time to be traveling, and lots to see and do along this route. See southern Arizona and New Mexico sites in another post on this subject:
Note: There is a Balloon Festival in Alamogordo and at White Sands National Monument this weekend (09/15 - 09/16/12)!