I have never encouraged or discouraged women in my parish from wearing a veil and when I am asked about it I say that it is purely their choice and whatever choice is made is fine. There are a great number of women in my parish who do wear veils to Mass. No one bats an eye at those who do or those who don't.
We also veil the chalice that will be used at Mass, by the way.
This is a great video, very positive and to the point. Catholic News Service is a division of the National Conference of Catholic Bishops: