The horses appeared to love doing it.
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I’m not so sure the horse ‘loved’ doing it, but some dog’s are known as water dogs so there may be horses that don’t mind diving in water as well. After all, some horses are quite acrobatic. Doing it safely would be a real concern for me. Whatever, the horse showed perfect grace in executing the dive. I was not aware of horse diving.
The first time I had EVER seen a horse do anything like that was in the movie “Hildago” (I think, but I might be mistaking it for a scene in “Second Hand Lion”) which had a guy back in, I guess in the 1880’s or 1890’s, a fictional account based loosely on the legendary long distance rider of mixed white and Lakota descent, Frank T. Hopkins, who in the movie, travels with his mustang Hildago to compete against the Arabs in a cross-desert race.
In one scene, and it could have been (and probably was) CGI, where the horse Hildago, with Frank Hopkins riding (Played by Viggo Mortensen) leaps from the wall of a castle into water below, an astonishing height, and I thought “No horse would do that!”
But...apparently they do!
Both “Second Hand Lion” and “Hildago” are very entertaining movies!
Horses are pretty amazing.
In wars, they apparently would, most of the time with little hesitation, do what their riders asked them to do, simply because being pack animals with the leader of the pack riding their back...do what was asked of them!
(This is just supposition from someone who has only ridden but never owned a horse!)