Horsepeople always say that the short-term memory (or attention span, whatever you want to call it) is in the ballpark of three seconds, probably less. That's why corrections and rewards must be given instantaneously for the horse to make the connection between cause and effect. We laugh at and then scold the person who gets bucked off, chases her horse around for 10 minutes, then gives him a whoopin' to teach him not to buck again.
Yet now, if we tie horses up for a couple hours after riding, they'll mull the training session over in their heads, reflect on what went right and what went wrong, and plan on how to do better next time?
Dead right. There is absolutely no training value whatsoever in tying up a horse for 20 minutes or 2 hours after a training session. It might teach the horse to just stand there, but its not going to help the horse understand any better what its supposed to do next time its been ridden.
Horses do not have a frontal cortex, the part of the brain required for insight, reasoning and complex thought- as a grass eater they don't need to strategise to catch their food. Training methods which assume that horses can plot, design, reason and plan into the future, or recall and re-examine past events demonstrate a fundamental lack of understanding about the limits of equine cognition.
Horses are extremely adept at making associations between cues or signals and outcomes they either value or wish to avoid and thus may keep on shying at the same spot in the arena months after getting a fright there, but they don't have insight into their behaviour and when tied to that pole, they aren't running through the training session they just had and working out how to do better next time. Horses have no insight into the things we get them to do when we ride them, they aren't seeing circles or patterns or good scores or the winning post, they are seeing/feeling pressures that come on and off when they move their bodies certain ways and in certain directions. And most certainly they are not thinking about how to annoy or please the person riding or handling them, though they may be trying to get the person and their annoying pressures out of their immediate space by bucking, rearing, shying, pulling back, not getting caught etc.
All tying a horse to a pole for hours on end will achieve is teach it to be tied up for hours on end. If that's the training aim you are seeking to achieve well and good but its not going to help them do a more rounder circle or jump higher the next time.
And the danger of tying horses up for hours is that they could develop what is called learned helplessness, where they learn that they can't do anything to relieve themselves of an unpleasant experience, like being hungry, itchy, thirsty, so eventually they stop trying. In experienments in dogs and rats, subjects who couldn't escape electric shocks eventually stopped trying to and when tested on new learning tasks afterwards most wouldn't even try to solve them, even when food was the reward. Tying a horse to a pole is not in the league of these experiements, but maybe that "humble" horse is simply dejected and miserable because he can't do anything to improve his situation. As a horse trainer its never a place I want any of my horses to be.