Western or eastern USDA 8?

Western....California Sierra foothills..

A very popular tree used here in Oz for just that purpose is Schinus molle. Most commonly seen in horse arenas, as well as for shade in dry, dusty sheep and cattle yards.

Of course I have no idea of your growing climate...

Fruitless mulberry is listed non-toxic for horses - can be a great fast growing broad canopy shade tree. Biggest disadvantages are that can require quite a bit of pruning due to vigorous growth and the male flowers produce a lot of pollen in the spring; not so good in a small yard, but maybe not so bad for a riding arena. We had one in northern California, so will probably grow well in your area. They generally stay healthy 40 to 60 years in north Texas.

Oh... also, they seem to be able to handle our Texas zone 8 100+ °F stretches without supplemental water once established, though will start to drop some leaves where not catching any lawn irrigation.

Honeylocust (Gleditsia triacanthos) pods are eaten by horses, people, and pretty much nothing else. You could plant them ad give your horses a treat. Might be hard to find a variety that is thornless but not seedless. `

Tuliptree (Liriodendron tulipifera) grows pretty fast, has flowers, and was recommended by a horse blog.