How old is too old to train a horse?

Any age could be good

As long as the vet feels the animals up to it and there are no health issues, I wouldn’t hesitate talking with a trainer.   I have known barrel horses that are well into their late 20’s before they retired.

My mustang apply was 22 when my 8 year old decided to use her for his gaming horse.  We retired her at 29 but she still ran circles around all the pasture horses.   I used her on quiet walking trails for a couple more years.  When time to turn her out she would prance and snort then gallop off to chase all the youngsters around pasture for quite a while.    I worried about her age but she never did.

We also had a logging Belgian that was retrained for light harness at 25.  Again a horse with tons of energy and little to no arthritis.  She drove my meadowbrook for about ten years, herr vision gave out before she did.  Once retired she ran the pasture with our Morgan and old apply,using the Appaloosa for her lack of eye sight.

Our vet said if the horse is willing and no pain or medical issues why not.   However with that being said yes the drafter was too old for heavy full day hauling and stump pulling.  I would never put an older horse to hard work.  You can tell pretty much if they enjoy what they are doing or hate it when your working them.

Could he learn it? Sure. But at 16, I wouldn't be teaching a horse to run barrels. Barrel racing is very hard on their joints, and he'd have a very short useful life doing it, and a good chance at being rendered unsound for other riding sooner than otherwise.  He's about the age most horses are retired from barrels, if they manage to remain sound that long. 

just try it and see and then you'll know