Here's some information on Arizona winter weather, from a resident. The temperatures vary with elevation (lower elevations have warmer temperatures), and there is generally about a 35° difference between the daily high and low temperatures. The average high/low temperatures in December and January for Tucson (elevation 2,400'): 65/39 and 64/38; for Phoenox (elevation 1,100')f: 67/42 and 66/41. February is a bit warmer than January. Of course, the actual temperatures will vary; a few days ago they were about 10° below normal. Camping would be quite chilly, but daytime temperatures are fine for riding.
The previous advice to avoid the higher elevations in New Mexico by dropping south to I-10 at Lordsburg (and continuing on it to El Paso) is wise. Riding on the interstate is okay when there are no alternate roads.