Mario Token Reward
In horse racing, if you go on the field, you may occasionally find a white bird sitting on the grass. This gives you a Mario Token, where there are 20 of them to collect. Once you collect the 20th one, another white bird will be found on the field. Opening this crate up will give you the Mario Token Crown, the final head accessory listed for your horse.
Star Characters
Beating Champion's Cup as a select character allows you to use Star versions of them, a more powerful variant of your character. Keep in mind that you have to unlock the Star character for each respective sport. For example, if you Star Luigi in one sport, it applies to only that one sport.
Grand Stadium...