So, after you've gotten a mastery level in a discipline, it shows up on your horse's info page, and there are scrolling arrows to move around. However, if you have level one in more than three disciplines, the arrows do not work at all. However, the talent arrows work even if there is nowhere to scroll. Only the last three disciplines to earn a level appear.
Additionally, training without being super happy or happy does not advance a horse toward mastery at all. You get the money and experience from training, but cannot reach the next level. This is problematic when you have an older un-retired horse with no cookies to give as treats.