Some answers to What do Hindu scriptures say about women headscarf (hijab)? on Quora.com cite these verses from the Rigveda that seem to suggest Hindu women should wear a head veil:
God made you women, so that you shall lower your gaze, do not look at men, keep your feet close, cover your head and do not disclose the garment, which should be concealed with the veil
(Rig Veda Book 8 Hymn 33 Mantra 19-20)
It's not good that a man covers his thigh with the female garment
(Rig Veda Book 10 Hymn 85 Mantra 30)
In Zakir Naik style, the guy in this YouTube video (Hindi) also quotes one of these verses.
What is the context of these mantras/verses? Do they really suggest women during Rigvedic times wore a veil to cover their heads and faces?