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.
So, you see horses in this position all the time and its natural?
They stand like that for hours and there are millions of pictures of horses being in that posture naturally?
Or does the horse put its leg back down on the ground when you let go of its leg? Why does anyone have to find ways of keeping a horses leg like they do to work on the hoof if its all natural to the horse?
So, again, you are making the horse do things that are not natural to its being. Power. Whether you use it or the horse gives it to you. And you are wanting the horse to put its hoof and leg in postures that it doesn't normally use. Who wins? You or the horse? Did you get the work done? You won.
And if you make the horse better then its a win-win. If you don't do the work because the horse was too much, you failed to do your job. Failure means a winner and loser. The horse won by keeping to its nature. It had the power to overcome a human trying to get it to do things it didn't want to do.
Contest between horse and man/woman playing out exactly like a contest between uke and nage in the dojo. Uke is pretending to have an aggressive nature and attack in some manner. Nage must alter that or be on the losing end of that attack. In aikido, the power is a means to appropriately match the attackers energy/attack and provide a win-win outcome. But it's still power and winning.