It depends on the breed of the horse. For example, the Arabian horse, because it was built for the hot desert, it has adapted to the climate and can go without food or water for a long period of time.
A horse will starve to death within a roughly 8 day period without food or water. The weather can affect how quickly this occurs and may shorten the length of time it takes to starve to death.
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First, they have short-haired coats so they don't overheat in the desert. second, they are able to go a long time without food or water. They are able to consume unusual foods in order to survive, like camel's milk. Last, they have stamina to endure a long trip.
Horses are not Indigenous to the Americas so they are not a traditional food source, but Native Americans did eat horse. During the US American Indian wars in the southwest, Natives would stock up on horses while traveling long distance. Some for riding, some as traveling food. As long as they had extra horses, they could settle for long periods without having to go out hunting.
Alexander had his horse, Bucephalus, for nearly 20 years.
8000 years
about 150 years