Here's a YouTube on it dated January. It's at 6,000' EL so in January, yes, you could have snow.
It looks like an absolutely beautiful place to be. Hope you make it!
Oliver Lee State Park is also close to White Sands Nat'l Monument if that will be one of your destinations.
https://www.youtube.com/watch?v=ZVeGvdC0kSEhttp://www.blm.gov/nm/st/en/prog/recreation/las_cruces/aguirre_spring_campground.htmlIf planning to do a lot in New Mexico in January it can be cold and windy so plan ahead. We had hoped to spend the whole winter touring New Mexico when we first began full-timing and it didn't take long to find out that it's cold, even at the southern part. We moved over to Arizona and much, much better. :)