Arizona/New Mexico in the winter--lots of questions!

I grew up in the mountains east of Albuquerque along I40. You will likely be able to find your window for snow-free travel in NM in January, but it could be really cold. I drove through Santa Fe in early January this year and it was 12 BELOW zero. Definitely not camping weather, but you may hit a warm spell (still below freezing at night), so you never know. Heavy snow falls above 6,000 ft sometimes in NM, but it tends to be dry for weeks at a time between big storms.