Yeah, but in Southern AZ I use to always worry about finding water for my horse. I could get enough out of cactus for me if I had to, but not for my mount (and at over 8 lbs / gal there's no way to carry enough with you for the horse). Ft Huachuca was "20 miles from water and 2 feet from hell".
In the east water is pretty easy to find. More often it's a pain having to ride to a bridge to get across, but the water is there. I remember crossing (ok, the horse stepped over it) the San Pedro River outside Sierra Vista that out east we'd call a creek
. More grazing along the way too in the east. Most of the area I rode in AZ always had a bumber crop of rocks, gravel and sand
so any weeds (if you find some) were quickly devoured.
Lot of room to ride, but easy to end up a casualty if you're not very careful from the lack of water and the search for grass.
I remember picking up a date once who told me I'd know her house because it was the only one with grass in the yard
(and she was right).