If you're staying somewhere in the valley, you will likely be ok. If you're renting a house up higher, especially on the ski mountain side of the valley, you could have problems with a good snow. During the Christmas storms this year, there were people stuck all over that part of the area. Don't know where you're coming from, but Mora generally gets much less snow than Angel Fire. I haven't had much trouble through the canyon there, although the 4 miles or so that's still one lane is alwaysinteresting. When you come out of the little canyon, the problem this year has been blowing snow and whiteouts for the first few miles in the south end of the valley. To be fair, with the big storm several days ago, that was also the problem between Eagle Nest and Angel Fire.
Short answer: depending on where you are staying and what the weather is doing, you might need chains.