Partly it’s just common vernacular of the horse world; one of those linguistic oddities particular to an industry. Another example would be “jumps good”. We are all educated enough to say jumps well, but no one does.
Equally though, ease of reference. No one is going to refer to their own horse, or one with which they have a long term or close relationship, as “it”, but, dealing with or speaking of hundreds of horses, way easier not to bother with gender unless there is a specific reason to state it. Speaking of someone else’s horse in a virtual forum, where there’s definitely no relationship? It’s essentially a hypothetical horse.
There is also a desired degree of detachment. You can’t try a horse without that, evaluate a horse professionally, or allow an attachment to develop to an animal that isn’t going to be a long term partner. That’s hard for people that are inclined to become attached to horses, which is just about everyone involved with horses, so a linguistic barrier sometimes develops, consciously or unconsciously. Sales horses, catch rides, horses that belong to flakey clients, horses that have lives over which you have no control; none of those can exist in the same mental space as personally connected horses without creating a very unhealthy mental state.
Thinking further, I don’t think one is inclined to gender any animal in speech without that closer relationship, but again that might be specific to people in animal related industries; I have no way of personally making the distinction. If I were describing a dog with whom I had no connection though I would definitely say “it peed on your tack room drapes”, even when, clearly, that dog is male.
