Trivia
The Kentucky Derby is a historical event, so there is plenty of history event trivia with which to build a game. Questions can be based off of past horses and winners, Triple Crown winners, or questions such as how long the track is, how long a race usually lasts, what the track is made of, technical terms or even questions about Churchill Downs and Louisville. Prizes can be drinks (mint juleps are the traditional drink), candy, treats or Kentucky Derby/horse trinkets.
Blindfolded Horse Drawing
Contestants are blindfolded and given a piece of paper and a pen. They are given one minute to draw a horse on the piece of paper (you can play music to pass the minute) and the person who draws the best horse is the winner. You can give out prizes to the winner and runners-up. You can also save these drawings year after year as funny mementos.
Stick Horse Races
You can conduct your own races around your house, in your backyard or down your street with stick horses. If you don't have any stick horses, you can make them (use socks stuffed with towels for the head, felt for the eyes, yarn for the mane, attached to a broomstick) or just use brooms. Have participants line up as if in the starting gate, and then send them off racing. Choose a spot to be the end of the course, and the first person to reach that spot is the winner of your mini Kentucky Derby.
Derby Pool
In Derby Pool, each person is assigned a number from one to 20 which corresponds to the horse they must cheer for during the Derby. To assign numbers, put folded pieces of paper with the numbers on it, and players choose their number out of a hat (or a riding helmet.) Winners can be awarded prizes.