Hey SRR,
I happen to live in NM and there are lots of places that what you are looking to do would work. The only thing is the money. I live in the northeastern corner near the small town of Raton, which is further north than Las Vegas. Some of the areas suggested to you are very much turist traps and living in those areas is expensive, Santa fe, Taos, Angel Fire, Cloudcroft are all very turisty and land prices are high. Although ranch land period is getting hard to buy, in my little corner of the state we have had a lot of speculators come in and buy properties for outragous sums and hold them for as little as a few months to a couple years and turn around, resale them for huge profits. We have had three neighbors sale out withing the last couple years. One place brought close to 600 per acre another brought just 200.
Where ever you pick to land there will be good and bad places.
Good luck and if you are in the area drop me a note.
TDS