Kentucky Derby Racing Game, 1950's by Whitman. This one has Citation so it is probably early 1950's. This is the plain version done all in cardboard with plastic horses. This is the deluxe version with a plastic covered game board and play money. Mini-Derby, 1970's by Shinsei.
Weighted horses vibrate down the track, miniature version.
Horse Racing, 1970's by Shinsei. Full size version of Mini-Derby, about 2 feet long. See You at the Winner's Circle, by JPR Games. Not dated but looks 1970's or earlier since it shows the old style tote tickets. Kuirakos Inc. Similar to Trivial Pursuit except all the questions are about racing.