The sad time for horses in the movie was before 1940. Alot of horses were badly hurt or died for movie excitement. A 1940 Jesse James movie 8 horses were killed by tripping them with wires. Let's hope now and in the future it won't happen again. Best efforts are done today to protect the horses.
Training is the key to safety.
Each horse has its hoof in sponge rubber to soften kicks and mouths are taped to prevent biting . Every precaution is taken in scene involving horses. To make the scene look more action packed it is filmed at a very slow speed then at regular speed looks fast and furious. When a horse fall is done preparations include digging a hole to fill with soft loose dirt to cushion the horse. Basically the horse stunts may be safer than for a stunt man.