Yugo hanging onto Chestnut for dear life to finish one of his races. Believe me, it's more awesome than it sounds.
Once Hachiken learns to trust his horse more in episode 3 of season 2, Chestnut does an amazing jump over a small fence that he earlier refused to. Although Hachiken falls off due to not being prepared, Chestnut leaps really high, causing some of the students to state they've never seen a horse go that high before. Hachiken, despite falling, is both amazed and humbled by the new experiences and views obtained when riding a horse.
Beppu. Just... Beppu. His facial expressions alone are awesome enough.