Does a horse shoe hurt the horse?

No the shoe that the horse wears protects the horses hoof from wearing down the toe.

The horseshoe is nailed into the hard part of a horse's hoof wall. That area feels no pain, similar to when humans clip their fingernails! There is a "V" shaped area on the underside of the hoof called the "frog" which IS sensitive when poked with a sharp object or they step on something very sharp.

But, be sure that you never attempt to shoe your own horse on your own. Unless you are professionally trained as a farrier, wait for a professional farrier to shoe your horse otherwise many serious problems could arise.

Another Answer:

A horseshoe, as mentioned above, doesn't hurt the horse when it is put on and stays on. However, naturally horses don't wear horse shoes and have been able to, for millions of years, sustain themselves and wear their hooves extremely well trodding in places where rocks, pebbles and stones exist. Naturally a horse's hoof is as hard as rock and worn down by the rocks and stones that they get their hooves exposed to. Many wild mustangs and other wild horses live in areas where rocks, stones and pebbles are frequently scattered over their range, they don't live in lush grassy areas like a typical ideological pasture everyone envisions.

As mentioned, nailing a horseshoe on a horse doesn't hurt it. But as several, if not more and more horse people have found out, horse shoes do chronically hurt the horse in the long-run. It's been found, and seen by a lot of vets that lameness issues and founder and other diseases may be linked to the fact that horses are, literally, forced to wear iron shoes. It's also been found that when a horse looses a shoe, he doesn't exactly feel "pain," but rather a sudden tingling sensation when he can feel his foot again after the circulation has come back--sort of like when you fold your legs too long until they get numb, then when you unfold them you get this feeling of "pins and needles" which is the blood and nervous tissue coming back to life again. Compared to domestic horses, wild mustangs, brumbies and other wild horses and ponies who have never worn a horseshoe in their entire lives are healthier and better off than those who have to live in a barn and wear shoes their entire lives simply because it's just been the traditional "thing." Also, though, wild horses have naturally tougher feet while some (most) domesticated sport horse breeds cannot stay sound barefoot.