You "make" a horse do something every time you work on its hoof. Ever see a horse stand on three legs with its fourth one lifted and bent? Do they do that naturally?
So, when you make the horse lift it's foot, you are, in essence, exerting a power over the horse to behave in a manner that is not natural to its being. It only takes that position because you make it do so. That is power. You accomplished the task (no matter how you did it) of getting that horse in a position it naturally does not use. (Yes, the natural function of the leg is such that it can be put into that posture, but the horse does not naturally stand on three legs with one bent back, upwards.) That is winning.
So, you are successful in your outcomes. Why is that? Did the horse stand on four legs and not let you do anything to it? You were successful in the outcome that you desired. That's the definition of winning. And you got the horse to do something which it does not naturally do (hold one leg bent with hoof upwards). That's power. Your successful outcome over the natural nature of the horse.
Now, *how* you accomplish that, as you stated, can make a world of difference.
For a horse it is quite natural to lift up its hoof. Just like it is natural to stand on three legs.
Making a horse lift up a hoof is not an easy task. If you try to use power to lift the hoof or to force the horse in any way (rope, chain, pully, whip, etc) the horse will only resist more and more. And next time he will remember what you did last time. He will have figured out new ways to resist you.
The true way to go with horses is what I practice in Aikido as well; connect with the other without fear and without exerting power.