Every freeway closes at times.
I-40 in December/January in the mentioned areas can be great, or have weather problems. All you can do is stay on top of the latest forecasts.
Odds are, I-40 will be fine.
And yes I-10 is a safer bet , unless it is closed for dust/wind storms between Deming NM and Wilcox Az
Scott and Liz - Southern NM
2012 Wildcat Sterling 32RL - w/level up (best option ever)
2007 Chevy 2500HD 4dr short bed Duramax w/allison
Reese Fifth Airborne air ride king pin coupler with Sidewinder