Is 5ft 8 too tall for a 15-15.3hh Morgan Horse?

No. You'll be surprised how much weight a horse can handle. If your just going to show it or go on trail rides i see nothing wrong with it. I'm 5ft 9 tall and weigh 125pd. My horse is 15 hands tall. and when we go out cutting trees i'll tie her up to the trees and have her more them. Some tree that we cut weigh up to 1,000pd. That's more then what she weighs. It just goes to show that horses are quite amazing animals.