Hi Cbrown2x- Hunted it once during thanksgiving, but never January. That unit doesn't really have true high country, and I'm not sure elevation makes much difference to the deer. There is definitely steep, rugged country in there though. Those deer have a bit of a desert mentality. You might find them up high on slopes, or down in the stuff that looks like antelope country. they like to lay at the tops of what locals call headers- where a draw meets the top of another ridge. they'll lay down against a pinyon or even a yucca, and watch everything below them.
As you go up the San Mateos, there's lots of low oaks, and the tops has more pines. The year we were there, the does were hanging in the pinyon juniper and low country more than the highest stuff. I imagine that's where the bucks will be in January.
One thing to note- I ended up with two flat tires in that country. the rocks are really sharp. cost me 600.00 to tow my truck and trailer into Truth or Consequences and get a new tire. That's hunting I guess. Good news is, there are deer in there. They can hide in what looks like it wouldn't hide a Jackrabbit. Just get to a good vantage point and use your glass. Walking around in there wears you out, and you end up bumping all the deer ahead of you anyway. That was my experience on the southern end of the unit. Good luck.