In real life, a horse doesn't automatically reach it's greatest potential once it's tamed and has a saddle. Horses should be able to be trained, for example, the more you ride it, the faster it gets, and the more it jumps, the higher it can jump, until it reaches it's full potential. Also, it will, over time, grow more affectionate, or begin to grow wild. If it likes you a lot, it will follow you at a longer range, so you won't need leads.
The idea is okay but I don't see much use for it. Horses vary in their potential from horse to horse as it is, and you actually can increase their potential with armor in some manner. I would rather see being able to change horses through equipment, that takes the armor slot, like horseshoes for speed, reins for better control, etc.
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