A person on a high horse is probably presuming to be more important than he truly is, or pompous.
In medieval times the height of your horse told of your rank in society and on the battlefield.
Knights rode high on horses bred large and strong enough to bear the weight of the man and his armor.
In ceremonial processions, kings and noblemen always rode the tallest horses, and anyone overstating his importance would be taken off his high horse.
