I think it is actually a chumra. Obviously, I was required to cover my legs when i was at the bais yaakov i went to, so i started doing it outside of school as well. As long as the whole leg is covered, either by your skirt being long and wearing knee highs, or by leggings and socks, or tights, you are following the minhag.
The denier concept is Super chumra, and the people that wear black tights/ socks from succos to pesach are taking their chumras to a whole different level that i respect, but feel is completely unneccesary.