Thing is, after years of going along with a friend on her trail rides - most people on horses, me walk/running or biking - I got talked into getting a horse. Now much as I like horses & being around them, I don't think I'd feel comfortable (or get much exercise) riding ALL the time, so I will probably spend a lot of time walking alongside the horse. (Which I've been doing anyway: she spent several years just loafing around a pasture, so she's rather out of shape & her feet are tender, and I've been walk/trotting her on a lead to get used to exercise & accustomed to me.)
So my usual trail shoes (waffle soles with no heels) aren't really safe for riding, while the boots I see are mostly of the "cowboy" kind, (Suited to walking from the hitching post to the saloon, IOW