California Code, Business and Professions Code - BPC § 19546

(a) In order to encourage and develop the racing of all horses in California, regardless of breed, whenever a fair conducts a program of parimutuel wagering, it may provide a program of mixed breed racing that includes thoroughbred racing, harness racing, quarter horse racing, Arabian racing, paint racing, Appaloosa racing, steeplechase races, barrel races, and show jumping races.

(b) All recognized breeds of horses may compete in barrel races, show jumping races, and steeplechase races. Parimutuel wagering may be conducted on barrel races, show jumping races, and steeplechase races at any public or private facility that has been approved and licensed by the board.