Cardinal Raymond Burke, Prefect of the Apostolic Signatura, basically the Church's Supreme Court Justice, has spoken on the matter, quite clearly. Recently, a woman wrote him directly, asking for clarification on this issue. He responded:
“Thank you for your letter …The wearing of a chapel veil for women is not required when women assist at the Holy Mass according to Ordinary Form of the Roman Rite. It is, however, the expectation that women who assist at the Mass according to the Extraordinary Form cover their heads, as was the practice at the time that the 1962 Missale Romanum was in force. It is not, however a sin to participate in the Holy Mass according to the Extraordinary Form without a veil.”
So there it is. If you are in Tridintine Mass (Extraordinary Form), it is expected that you wear a veil, but in the ordinary form, do whatever you like! If you do desire to wear a veil, there is a real dare to veil campaign going on, interestingly enough!