I used to live in Tucson and the only cactus problem I had was the friggin' cholla. I had one mare who just would not leave that stuff alone, so I was always having to pull the spines out of her nose. To this day she's not happy with having someone mess with her nose. I lived up near Miraval, so we had elevation but still plenty of cactii. Never had a leg or hoof problem, just the dam* cholla in noses.
As for the barn, I suppose they could leave the floors unbedded and the horses only go in when it's storming. The packed dirt in their runs is plenty cushy enough, they can be plenty comfortable on sandy dirt. Same thing in the corral. I would have put some shade covers on it but they'll be ok.