At least with horses, the hoof is cup shaped and made of the same material as horn. The outside layer is like a fingernail, as you go deeper into the wall or the sole of the hoof, you get into live tissue which has feeling and can be bruised etc. Inside that is the coffin bone, which evolved from toes which the horse had back when it was about the size of a dog, and had more of a pointed upper lip and different teeth so it could eat fuit and leaves off of trees and bushes. As it evolved, it got bigger, the toes became less prominent, and the upper lip took on a the squared shape it has today as the horses diet changed from it being a browsing animal to it being a grazing animal. Eventually the hoof developed along with the other parts of the body to its present day form. Which makes it a wide ranging grazing animal that might walk up to 20 miles a day as it eats.
As for knives, there is a special knife, called a hoof knife,that is used in conjunction with a few other tools to trim a horses hoof. Wild horses hooves wear naturaly as they grow, but with domesticated horses, you have to trim them. It helps maintian the correct shape and angles to keep the horse healthy and allow it to perform whatever duties it needs to without going lame.The knife used has a chisel ground edge which is slight bent to the side.The tip is bent compltely over to form a gouge at the end. The bend of the knife allows you to slice out the excess growth in the sole of the hoof to maintain a the right shape. The gouge shaped end is to trim away excess growth in the bars, which are the V shaped grooves in the bottom of a horses foot.
I don't know what's involved in trimming a sheep's hoof or foot, but I'm guessing that that's what a sheepsfoot blade was originally meant for but has become a popular blade style for utility as well, and has probably been changed some over time.
Geez, didn't mean to take so long saying it
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I may not be the sharpest knife in the drawer... but I've got the sharpest knife in the room.