Gymkhana is a term used in the United Kingdom, east coast of the United States, and other English-speaking nations to describe an equestrian event consisting of speed pattern racing and timed games for riders on horses.owever, the term gymkhana is used in California. Gymkhana and O-Mok-See classes include timed speed events such as barrel racing, keyhole race, keg race (also known as down and back), flag race, and pole bending.