Well, New Mexico is a huge and very diverse state. You can ride desert down by Las Cruces to the tightest woods you could ever want up in the Taos area. Just depends on where you're going to move. Me, I live in the very far NE corner (No, not Farmington, that's NW) and I have a lot of trouble finding riding buddies, so I tend to go places where there's other people riding rather than go exploring deep woods. I would sure LIKE to do the woods thing, but it's a 3 hr drive, minimum. In that same 3 hrs, I can go to the Canadian River just north of Amarillo and ride desert-type stuff, or I can go north to Pueblo CO. Where I'm at is very open grasslands and the riding is not extremely exciting, although I'm not complaining- I CAN go riding, at least. But to do anything different is a 3-hr drive.
Now, if you were in the more central part of the state, it would be different. From Albuq, it's easy to do desert stuff just outside town, MX in Moriarty, or woods up in the Los Alamos area, all easily w/in 2 hours, most w/in 1 hour.