It's not usually part of the history lessons, but the availabiliyt of food for the horses has always been a real factor in any military campaign involving cavalry.
Can you imagine the logistics for really large military movements , such as the American Civil war or any of the 18th or 19th century wars of Europe where thousands of horses were needed.?
If you didn't have food for the hroses, you didn't have an army.
That was one reason that Chief Joseph's band of Nez Perce indians were able to outrun the US army for such a great distance during the summer; their horses were used to living off the land and there was plenty of forage. The Army animals were used to being corn fed, and when they moved quickly, they outran their food suppliers and they struggled to maintain energy on local forage, whereas the Indian ponies flourished. But, when winter came, the indian ponies were on such lean times (they were usually not ridden much inthe winter) while the big Army mounts had corn wagons to keep them in calories.
This isn't the only reason Chief Joseph was forced to surrender, but it played a factor.