Is it permissible to wipe over a headscarf wrapped under the chin if it is worn over another piece of cloth that covers only the head, without covering the ears or the throat?

A woman is permitted to wipe over her head covering (khimar) during ablution (wudu’), by analogy with the Prophet’s (peace and blessings be upon him) wiping over his turban ('imama) and leather socks (khuffayn), since the underlying reason (illah) is the same: to alleviate hardship. Moreover, it is not a condition for the head covering to be directly in contact with the head; it is sufficient for it to merely cover it.