I think we can safely rule out
hedge soles, as they would have made walking rather thorny.
As for the wings, the fact that he still relied on Gwaihir for aerial transportation seems to indicate the contrary; also note that when the time for him to return had come, he went home by ship, not by air. So if there were any wings at all on his boots, they would have been purely decorative.
Or maybe his boots were so highly polished that the highlights from the shoeshine created an
illusion of white wings?