How high can my horse jump?

My 14.2hh 16 year old welsh section D clears 3'9" so I'd say that there is definitely the chance that you'll be jumping bigger! I recommend working well on the flat to build muscle, and try raised trotting poles. As for height, go up higher a little bit at a time. Rather than going higher and higher during one ride, spend a few rides at the same height before moving up. This will allow the horse to become comfortable and confident with what its doing. If it knocks a pole, try again instead of leaving it on a bad note. Remember to praise the horse so that it knows it has done what you've asked :) Good luck!

completely up to horse and rider train him up slowly and eventually youll reach a limit your both comfortable with just dont push him to much if you dont feel that your both safe.

You'll need to slowly train him to jump higher. So if he can jump 3ft try adding a little height. Don't make it too high or your horse will definetly spook.