As I understand it, using the 1962 Missal doesn’t mean that you’re bound by the requirements of canon law that existed in 1962. So it would be wrong for anyone to think that women can choose not to cover their heads at an OF Mass, but are obliged to cover up at an EF Mass. The only difference is that those who attend EF Masses are more likely to be traditionally-minded and conservative. At my Catholic college, I often saw girls wearing veils or hats to OF Masses on campus.
That said, I think that if a woman were to go to an EF Mass and feel motivated by the reverence of the liturgy, the piety of the congregation, or whatever, to wear a head-covering, that’s quite commendable. Personally, since I don’t consider covering my head to be a positive obligation, I try to follow whatever seems to be the custom in the community. So when I go to the EF Mass near me where all the women cover up, I bring a hat or veil - and when I go to Mass in other places, I don’t (unless I happen to be wearing a hat already).