A young lady may wear whatever color best complements her. I remember back before the chapel veil was discarded the only time I saw white was when someone forgot her veil and pinned a klenex on her head (and, back then, all klenex tissues were white).
However, in many people's opinion, white is most appropriate for young girls and unmarried young women, while black and other colored veils are best for married women. My wife and girls mostly wear the small black veils, though they also have pink veils (that they wear twice a year) and blue veils (that they often wear on or near feasts of our Lady).
They also have some headscarves that were given to us from someone stationed with the U.S. Army in Afghanistan and we've found that if you don't wear it like you see Muslims wearing them they don't look the least like Muslim head-dress. These are in a variety of colors and we have several so that they can wear one, if they like, that matches their blouse or dress. Often, though, they wear a veil and use the headscarves as shawls when it is chilly.
My eldest daughter wore, for a time, a very nice, modest dress hat (it was mostly white) until she decided to enter the convent at Mount St. Michael's. There are a couple of young ladies at one of the chapels my family attends who always wear a hat.
Bottom line: Women don't have to limit themselves to white or black veils and they don't even have to limit themselves to veils. They are to cover their heads, but there are many ways to do so that give glory to God.