I knew a lady in Wyoming who did long distance races on horseback, 100 miles was typical. She said every 20 miles there was a vet stop to check the T of the horse, and if it was high you were DQd. I asked if they checked her T and she laughed.
She said she had to lead the horse a certain part of the journey, especially up hill, and it was grueling. I chuckle at Westerns that show folks galloping long distances, a horse simply can't do that. A western antelope can though, amazingly for an herbivore.
As my lead character in my books was usually mounted, I had to sort out how far he could go in a "normal" day. I made some comments about getting grain to feed the horse when possible. Herbivores normally are quite inefficient at getting Calories.