'Ol Gabe here, I imagine Major 2 will recall the following...
Although not a film about the American West, etc., the '70 version of WATERLOO starring Rod Steiger and Christopher Plummer was loaded with horse action and dozens of scenes with them falling as 'shot'. The Union Brigade cavalry charging across the open plain showed those closest to the camera falling as shot by cannon fire from the French batteries. You don't have to look close to see how it was done as the horses were trained to fall forward and collapse when the rider wold pull up on a rope/strap attached to the right front leg, giving the visual impression that the horse had been killed and was crashing into the ground. Many of the soldiers/riders did this stunt and it is easy to see it when it happens. Hundreds of horses were used in the making of the film as British and Allied cavalry and French units seen in waves attacking the British squares on top of the hill behind Wellington's original position. In the film, when the French attack the squares, Wellington is heard yelling to the troops, "Shoot the horses!" In effect by doing this the dead animals would create a barricade to help protect his troopers in the squares. As an aside, Marshal Ney, Napolean's cavalry commander, led several charges of French cavalry and was himself shot off of at least four horses, some say five. Unwounded, he grabbed the next available running riderless horse and continued the charge.
It was an immense and impressive production using several local nations ceremonial cavalry to make up the British and French units, the viewer seeing several thousand at any given time on the widescreen as many were in the background and waaaay back on the vast open set, the director used many as visual filler to give the impression of a gigantic battle, which it truly was.
Another series of films using 'dead' horses was that of the Custer legend, both cavalry and Indian ponies crashed.
Hopefully this may generate several remembrances of other films using the same or like methods of stunts.
Best regards and good viewing!
'Ol Gabe