That's something I hadn't thought of directly, but it's very true.
My wife is a horse trainer & riding instructor and one of the first things I see her teaching is being decisive and clear about what you want the animal to do. The parents of her younger students (mostly girls) often report that their kids become much more confident after taking lessons.
Horses are very finely attuned to body language and don't respond very well to someone who is timid and uncertain. The flip side of that is, of course, if (s)he really doesn't want to do something, come hell or high water, it ain't happening!
I don't understand how you're making the jump from "leading a horse is like leading a team" (which is easy to agree with) to some point about morality.
The qualities of good horsemanship are essentially moral and physically cultivated qualities, and among those is the ability to be recognized as a leader and followed willingly by another creature in nature.
I am saying the qualities that people recognize as leadership and follow willingly, are moral qualities that can be developed and taught, and there is a history of those being taught through horsemanship.
Patience: it's an animal, it doesn't care what you want, but with work and education, you both transform.
Perseverance: incremental work, with a living being that isn't subject to reasoning, is what makes the most change.
Ownership and Obligation: the animal is your responsibility, it does not have responsibility, you own your failures.
Decisiveness: related to ownership.
Benevolence: xenophon's "nothing forced is beautiful," and (I think la Guerieniere's) "ask much, be content with little, reward often." exemplify these.
Takt: the ability to express your intent simply, unambiguously, consistently, and with a stable emotional presence.
Temperence, moderation, and sympathy: this is a living thing you can't just threaten into submission.
Magnanimity: the animal is going to test you constantly, and you have to be greater than it.
There are other aspects that the words we use today have been freighted with inaccurate critical interpretations, but they are similar to the Aristotelian virtues.
These (among many) in addition to exercising the physical experience of leading, which means to be followed willingly. You learn how you don't just read about something and become it.
Going back to Xenophon (and Simeon before him), who wrote one of the earliest surviving treatises on horsemanship, the personal qualities it takes to ride and train were also the basis for leadership. Xenophon's work on the Cavalry General is mainly practical and tactical, but expands on some of the principles of horsemanship - a key one being, "nothing forced can be beautiful."
The essence of it is that because they are prey animals, good horsemanship is necessarily an exercise in leadership.
Dom Duarte's 13th century treatise (next on my list) is also about the moral qualities for horsemanship, and the classic "education of the king," by Pluvinel is about educating the king of France as a horseman, with an eye to developing the king as a leader.
IMHO, officer training has always included horsemanship because it develops a kind of physical presence and fearlessness required to get people to follow them willingly.
Glad to see something like this mentioned on HN, as revisiting the cultivation of leadership through physical and moral exercise is something we in tech could certainly benefit from.