Horse 'leg finger' (or toes) are called 'hooves'. One is a 'hoof'. All of them are 'hooves'.
One leg on each side of the horse is called straddling the horse or the straddle!
the leg markings on a horse are called socks and stockings.
It is called a chesnut.
If a horse has hurt his/her leg the horse will be called lame till the leg has healed . If the horses leg is very badly hurt it may have to be put down (die) . But if it is just a minor injury you should keep the horse in his/her stable he/she stops limping.
I think this question is refering to what is know as a "leg aid". It's not so much a kick as leg pressure to direct the horse to what the rider wants him to do. Well trained horses should always understand leg pressure which can be heels, calves, thighs or butt (seat in horse talk).
It's called a hoof. It's at the end of each of its four legs, which is called a foot or hoof.
Charley horse (or Charlie horse). Also variously called a corked thigh, dead leg, granddaddy, chopper or Tommy horse.
Ergot. It is very similar to the chestnuts on a horses leg, and they have no nerve endings. they can be cut off and the horse will not feel it.
The growths on the insides of a horse's legs are called chestnuts. They are what remain from the ancient horse's multiple toes. They do grow and you can peel them off; they don't hurt
The area above a horse's hind hoof is called the fetlock joint. It acts as a hinge to allow movement in the horse's lower leg.
Stanky Leg Syndrome
There are several different joints in the back leg of the horse. The joint high up near the flank is called the stifle joint. Next will be the hock, the 'backward knee' half way down the leg. At the bottom right above the hoof is the ankle joint.