At the main menu hold in the R3 button and quickly press Up (2), Left, Right (2), Down, Circle Circle. When you start a game, the horse will be riding on the back of the jockey. Note: It is almost impossible to win a race as the jockey can't run very fast due to a horse being on his back.
Konami / Nintendo Snake Jockeys
At the main menu hold in the R3 button and quickly press Down (2), Left, Right (2), Up, Circle Circle. When you start a game, likenesses of Hideo Kojima (creator of Metal Gear) and Shigeru Miyamoto (Super Mario creator) will be riding snakes. This is an injoke because the two collaborated on the GameCube version of Metal Gear Solid: The Twin Snakes.
Monkey Jockey
At the main menu hold in the L3 button and quickly press Up (2), Left, Right (2), Down, Circle Square. When you start a game, a monkey will be riding on the horse.
Picking Winners
Look at the leg type of your horse before the race. If it is a front horse, you need the best possible start, so get the speed markers to match exactly if you can. Then you dont have to waste energy getting in position. Preceders need a very good start as well. Middle horses can find it difficult to get in position with too good a start, but you dont want it to be too bad either. Closer horses need a start that is not perfect, or you will end up at the wrong end of the pack. Stay in position until the last corner, then speed up. Use the whip when you are on the straight. Use the whip once, then wait for the gauge to fill up completely before using it again for the best results. Try to get a horse with good breaking speed, heart and stamina when you select the horse. You will also need good power when you race on a track with an uphill slope on the final straight.