I think it really depends on the individual horse. As long as arthritis and such isn't an issue, there isn't really a "cut off" age. You may have to decrease the height and how often you jump as the horse ages though. Posted via Mobile Device
Whenever your horse starts to be physically unable to. Off topic, but I think you over estimated the height of your horses. 19 and 20 hand horses are very hard to come by in lighter breeds like the ones you posted.
Exactly as others have said; it depends on the horse.
Last year I was competing a 26 year old horse through 3'7" and schooling through 4'. He was happy, sound, and enjoying it. However the majority of horses can't continue jumping that high when they're 26. There's also always maintenance involved with older horses. This horse in particular that I rode needed hock injections every 6 months (not too surprising, considering horses half his age are on a schedule like that) and was also on a joint supplement (also not surprising).