Conversation so far:
what type of hoof does a horse have
A horse hoof is a structure surrounding the distal phalanx of the 3rd digit which is covered by complex soft tissue and keratinised structures.
Where does a horseshoe get applied?
Horseshoes are attached on the palmar surface of the hooves, usually nailed through the insensitive hoof wall that is anatomically akin to the human toenail.
Does putting horseshoes on hurt the horse?
Since there are no nerve endings in the outer section of the hoof, a horse doesn't feel any pain when horseshoes are nailed on.

Question: Does the hoof grow?
Self-contained rewrite: Do horse hooves grow?