It both is and isn't to my mind and experience with horses, Butch.
Many of the trails are horribly rocky and uneven, requiring a horse and rider to negotiate ledges, both up and along, with multiple high steps and much high exposure to cliff edges. Any horse that is the slightest bit sketchy temperament-wise can get in a bad situation in a hurry. Even if you manage to stay on the trail, every darn plant seems to be full of nasty thorns or spines.
Even down in the flatter parts of the desert, the hazards from cactus spines mean the rider must wear heavy leather or armored nylon chaps, in addition to sturdy boots. Stirrups have to be of the enclosed style. Almost every horse or mule I encountered on the trails showed some scarring on the lower chest and the fronts of all four legs. I saw one riding mule easing along in no apparent distress, with 15 or 20 long cholla spines sticking out of her left rear thigh. Situation normal, I suppose. And to be able to keep a horse or mule watered can be a real challenge in that country. This is a particular and potentially dangerous problem, for sure.
On the other hand, the ability to carry several gallons of water on a horse vs. a few liters for a hiker is a great safety advantage. To be comfortable with 20 or 30 miles of trail ahead, rather than the 8 or 10 that hits my easy day hike limit opens up enormous territory for exploration. For a rider, sitting up high sure gives a better view.
Like the tent vs. RV discussion...pros and cons, pluses and minuses on both sides.