My quibble is , and horse lovers will agree, that the author's assertion that small grass fed ponies are "faster" then shod, grain fed horses is simply contrary to fact. Whether by, "fast" the author means actually quicker in the run or simply being possessed of more endurance, a shod, grain fed horse will surpass a grass fed pony, all things being equal. And this is true summer or winter, although in winter the pony would need more grass for heat when little is available and have very little extra energy stored up to spare for exertions, and in summer, although grass would be more plentiful, the campaigning presumably harder.
In fact in my reading of the Indian wars it was the ultimate superiority of the Army horses that gave the cavalry a great advantage and that superiority was expressly attributable to these factors. I note that the author does not explicitly make the case that Miles was tied to his supply tail while the Indians were not. But this is a different argument.
An unshod horse will break down in hard riding over rough country long before a shod horse and he will play out sooner than the grain fed horse. You simply can not get uninterrupted hard work out of the grass fed horse for days on end. There simply is not enough energy in the grass. The horse would have to spend the bulk of the day grazing to accumulate enough energy to make up for yesterday's exertions as well as tomorrow's. I would further assume that in campaigning, the Indians would be unable to bring with them a herd of replacement horses.
Excellent point that you make, and something that I hadn't considered. I think the author was saying that the Indian ponies were more mobile, which is not exactly the same thing. Mobility takes-in a range of characteristics: speed, agility, range, endurance, etc. Guderian made the point that the engines of his tanks were as important as it's main armament.
When you decide to attack their encampment... you will find their 'herd' nearby. One would also concur that in battles initiated by hostiles... additional mounts would be brought along if only to compensate for attrition.
Grain-fed, 1200-lb. animal toting 160-lb cavalryman, 30-lb. McClellan saddle, Springfield Carbine, saddlebags, bedroll, canteen, picket-pin, etc, etc.
Grass-fed 800-lb animal toting nearly naked 160-lb Indian with loaded Winchester.
Horse feed ties the cavalry to a supply train. Horses are designed to live on grass. Horse feed is a high-energy dietary supplement that boosts their performance, but ruins their ability to thrive without it.