It's possible but will depend on the conditions. Human's greatest advantage is in hot and dry weather. Because of the ability to cool down with our sweat while exercising, we can endure much more than many animals. It is possible for us to stay cool at speeds and distances that would cause other animals to get overheated.
If the horse gets overheated, he can suffer of a heat stroke which can be fatal. If you see your horse showing symptoms of heat exhaustion (sweating, panting, hot skin) get him in a shaded area and offer him some water. If he doesn't respond to this treatment, it's time to seek veterinary assistance.