If it were an established custom
It was an established custom for women to cover their heads (how they covered them varied by culture or location) when in a church (which includes the choir loft). As with so many other long-held customs, it was tossed when the "spirit" of the council was implemented; ignoring the fact that the council fathers said nothing about changing the custom.
Our choir doesn't have vestments. The men in the schola wear cassock and surplice on the rare occasions when the schola sings in the sanctuary.
However, if a choir is in vestments prescribed by the church, and those vestments are uniform for men and women, then it makes no sense for some of the women to wear a veil . . . then they're out of uniform.