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New Mexico law allows tire chains when necessary for safety, so the onus is on you to demonstrate the need.
We had a house in Angel Fire for 10 years and never used tire chains. In fact, I only recall seeing a couple of cars with them. The state/county does a good job of keeping 64 and 434 clear and passable with 4WD or AWD. The resort does an excellent job of keeping roads and streets clear in the village proper. Our house was nearly 2 miles off 434 and we never had an issue getting to and from it in an AWD SUV. The driveway to the house, well that was another matter.