With care and consideration, horses can be good athletes into their teens. A study at Rutgers University in New Brunswick, New Jersey, compared heart rate and cardiovascular changes between young horses and middle-aged horses (horses in their teens and up to age 20). The study showed that there was little difference between these age groups. These physiological capacities decrease somewhere around the early 20's, But this doesn't mean that a horse past his 20's can't exercise. You just have to take extra caution.
One of the issues for horses in their 20's discovered in the Rutgers' studies concerned thermal regulation. Older horses don't have a large enough plasma volume so they won't have a reserve large enough to sweat efficiently. Although sweat will be evident, the blood can't move through the skin as well and the sweat won't cool the body down quickly enough. Also, the amount of fluid within the body won't be as plentiful so a horse in his 20's can run the risk of getting dehydrated faster than when he was younger.
The older horse can handle the exercise but he will have trouble handling the combined effects of trying to stay cool on top of the exercise. For the older horse we may have to back off the intensity and the duration for a little bit. For instance, instead of going at a fast canter for an endurance ride he may have to do some of this at a trot. Although age breakpoint isn't really known, be aware of this decrease when your horse is in his late teens to early 20's. Expect your horse to heat up faster and his heart rate to increase quicker. He will also breathe harder. But the good news is that he should recover easily, in fact, ten minutes later he should be back down to the same level as he did when he was younger and be able to continue. Rule or thumb: don't push as hard and take longer to cool down between sessions. And this is all contingent on whether your horse is orthopedically sound