Good horse racing games for kids include "Horsey Game" and "Horse Training." Both of these games are available to play online at Pet Games Online.
To play "Horsey Game," click the left mouse button to start the race, then click the left button once to jump and double click to jump higher. "Horse Training" requires the player to buy a horse, train it and feed it before racing. To make the horse run faster when playing "Horse Training," press the Space button on the keyboard to cause the horse to sprint, then release it when the horse begins to get tired.