Horses grow at the rate they grow and grow to their genetic potential as long as their needs are met nutritionally. You don't want to push growth or you can cause debilitating joint problems. There are no guarantees to the height your horse will meet at maturity. If you are looking for a specific height then purchasing a horse that is that height is the only way to guarantee you get it. I know plenty of pony sized quarter horses. Nothing wrong with them at all.
Some horse people change their horse, they change their tack and discipline, they change their instructor; they never change themselves.