Hello there karewhit! Welcome to the forum!
I don't live in New Mexico and I haven't gone camping there, but if I were you I'd check with the Back Country Horsemen of your area-they do all sorts of trail rides and camp outs. (At least in my area, but I'm pretty sure that goes for any area) I do believe you have to be a member to go with the Back Country Horsemen, but I'm pretty sure it doesn't cost that much. Hope that helps a bit. Good luck!
"We were ninety-nine percent trouble and one percent innocent...What could we say? We were adventurers!" -The I Can! Cowgirls
"I'm not a horse trainer, I'm a horseman. What’s the difference? A horse trainer trains horses; a horseman trains himself." – Chris Cox
"How do you gain your horse's respect? By moving his feet forwards, backwards, left and right and always rewarding the slightest try." -Clinton Anderson
“It’s the way you ride the trail that counts.” -Roy Rodgers
"Even if you're on the right track, you'll get run over if you just sit there." - Will Rogers