All horses can go barefoot, if the right holistic management is attended to. No horse NEEDS shoes.
HOWEVER, I don't disagree with much of what has been written above. It depends on a lot of factors - quality & frequency of trim, diet, environment, conditioning, to name a few - as to whether a horse can develop tough go anywhere, do anything feet. Most horses are managed in a less than ideal manner in this regard and so they generally need some protection on some surfaces.
Hoof boots are fantastic for this purpose, providing true protection that a rim of steel can't. Some horses & work requirements are inappropriate for hoof boots tho, and in that case, metal shoes may be the best option.