I really don't think there should be a problem with growing tall bearded, intermediate bearded and border bearded irises in Las Cruces, and I think there are people in the iris forums who live there (although I really can't think of anyone right now, of course!). But irises are pretty finicky -- and the little dwarf SDB irises need some freezing nights in the winter in order to bloom the following spring. And the beardless ones are totally different and I really don't know much about them because those I can't grow here. But the bearded iris, other than the SDB's, really should grow there. We get over 100 degrees for at least a month each summer and 95+ for the rest of the summer and through September, and you need to bury the rhizome most of the way into the dirt and half-day shade is really good for them -- and fertilizer is the big thing. After you've grown irises for a year or two in the ground they will have sucked up absolutely all the nutrients in the soil around them, and then you need to fertilize in the fall and early spring or they'll never bloom again -- but with a low nitrogen fertilizer. I get Pennington 6-10-10 for less than $3/box and it really works! Oh yes, and you need to split up the clumps every 3-5 years because they will stop blooming if you don't. Many times people end up with large clumps with fantastic leaves -- and no flowers, and that can also be from over-fertilizing. As I said, iris are pretty finicky. But oh what beauties you get in the spring!
Sorry -- I know this is the Roses Cubit, but I couldn't resist. All these are tall bearded irises growing in Bakersfield in the spring.