As it's already been said, it depends on the individual horse and how that horse has been taken care of throughout their career.
So there's nothing wrong with running that 17-year-old champion barrel horse you saw on Craigslist as long as he is physically fit and sound to continue doing so. And most often, and older quieter horse is perfect for someone who is just starting to learn the barrels. The hose is experienced and knows his job so that the rider can focus their attention on themselves and their riding, since the horse already knows what to do.
I too have seen a lot of horses who are hurting that either need vet care for their problems or need to stop running. Unfortunately, it is a free country and people can do what they want with their horses.
But as long as the horse is taken care of properly, they can most certainly be able to run barrels all their life and into their 20's.
∞•*˚ Βгįťţαňγ ˚*•∞
It is not enough to know how to ride; one must know how to fall.