There's always more to be said, but I have an answer on veiling in Ancient Greece that may interest you: Is it true that women in the ancient Mediterranean often wore veiled clothing similar to the Middle East today? While the dates in it don't come up to the first century CE, the source I used notes that the dress traditions continued into the Roman period. (In general, the texts I am aware of on Greek dress only deal explicitly with what was worn before the rise of Rome.)