Women should still wear veils while in the presence of Our Lord in the Eucharist. Why? Even if the Code of Canon Law does not apply, St. Paul's words in 1 Cor. 11:4-6 do still apply:
Any man who prays or prophesies with his head covered brings shame upon his head. But any woman who prays or prophesies with her head unveiled brings shame upon her head, for it is one and the same thing as if she had had her head shaved. For if a woman does not have her head veiled, she may as well have her hair cut off. But if it is shameful for a woman to have her hair cut off or her head shaved, then she should wear a veil.I wanted to share this as well:
"Women are definitely more mysterious than men, not only because their affective life is more complex and more refined, but especially because there is something in women that calls for veiling. It is not by accident that women traditionally wore a veil, and that, up to Vatican II, they wore veils in Catholic churches. This custom was deeply symbolic, and alas this symbolism is now lost. Under the influence of feminism, many Catholics were led to believe that veiling indicated some sort of inferiority, and for this reason it was abolished.
This interpretation rests on a misunderstanding. Far from indicating inferiority, the veil points to sacredness. While we do cover what is ugly or decaying, we also veil what is sacred, mysterious, and sublime. When Moses came down from Mount Sinai, he covered his face to hide the glow that was apparent because God had deigned to speak with him: Moses' body reflected the depth and mystery of his experience.
Every woman carries within herself a secret most sacred, mysterious, and sublime. This secret is life. Eve means "the mother of the living." In the mystery of the female body, human life finds its beginning: not in the male semen but in the fecundated egg, hidden in the cavern of the female body. There God creates a new soul which is exclusively his work, and in which neither father nor mother has a part. This creation takes place when the male seed fecundates the female egg. Thus at that very moment a closeness exists between divine action and the female body which marks the latter as sacred ground. This is why the way a woman dresses, the way she sits, walks, laughs, should always be marked by a note of holy reserve. A woman conscious of her unmerited privilege will necessarily adopt a bodily posture- what is today called body language- which adequately reflects this calling."
-Alice von Hildebrand, from the book Women and the Priesthood