Thoroughbreds (movie, 1944)

Sgt. Rusty Curtis of the U.S. Cavalry is unhappy about the Army's plan to replace horses with tanks so, after a medical discharge, he tries to buy his old military mount Sireson. Unfortunately, the father of wealthy socialite Sally Crandall outbids him with plans to train Sireson for a steeplechase race. Sally and Rusty develop a rivalry because she has a favorite horse of her own, but when her horse is hurt she and Rusty declare a truce and begin a romantic relationship.