Mind you, I am not very picky about women wearing veils at Mass (but I think they should)…., but some were/are : The pagan women of Arabia will be your judges. For they cover not only the head, but the face also. . . . But how severe a chastisement will they likewise deserve, who remain uncovered even during the recital of the Psalms and at any mention of the name of God? For even when they are about to spend time in prayer itself, they only place a fringe, tuft [of cloth], or any thread whatever on the crown of their heads. And they think that they are covered! (Tertullian: Veiling of Women). Also, Paradoxically, IMHO, it makes women look even prettier for some strange reason, maybe just an outward sign of womenhood? Kind of like dresses instead of pants.
Our Lady of Mt. Carmel procession (Italian quarter of London)
Lord of Miracles Procession in Peru