Mustang Tag
One player is the designated "wrangler" and the other players are the mustangs. When a Mustang is tagged by the wrangler, that player becomes the new wrangler and so one. Ensure fair play with this game to avoid one player being tagged repeatedly.
Horse, Horse, Pony
Play this party game just as you would Duck, duck, goose.
Play the Story Game
You probably remember this concept from Girl scouts or Sunday school.Sit the players in a circle. Have several theme words written a head of time on small slips of paper:Wild Pony, In the meadow, It was a winter's eve etc.The first person selects the theme...starts the story with the first phrase and then each player continues the story one phrase at a time.