Bilal reported: The Messenger of Allah, peace and blessings be upon him, wiped over leather socks and head coverings in ablution.
Source: Ṣaḥīḥ Muslim 275
Grade: Sahih (authentic) according to Muslim
Ibn Taymiyyah said, “Since it is permitted for men to wipe over clothing on the head, so is it permissible for women as it is for men. As it is permissible clothing for the head, which is usually difficult to remove, it is similar to the turban of men. Moreover, her veil covers more than the turban of men, it is more difficult to take off, and her need of (the concession) is greater than leather socks.”
Source: Sharḥ ‘Umdat al-Fiqh 1/266
عَنْ بِلَالٍ أَنَّ رَسُولَ اللَّهِ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ مَسَحَ عَلَى الْخُفَّيْنِ وَالْخِمَارِ يعني في الوضوء
275 صحيح مسلم كتاب الطهارة باب المسح على الناصية والعمامة
قال ابن تيمية وَلِأَنَّ الرَّأْسَ يَجُوزُ لِلرَّجُلِ الْمَسْحُ عَلَى لِبَاسِهِ فَجَازَ لِلْمَرْأَةِ كَالرَّجُلِ وَلِأَنَّهُ لِبَاسٌ يُبَاحُ عَلَى الرَّأْسِ يَشُقُّ نَزْعُهُ غَالِبًا فَأَشْبَهَ عِمَامَةَ الرَّجُلِ وَأَوْلَى لِأَنَّ خِمَارَهَا يَسْتُرُ أَكْثَرَ مِنْ عِمَامَةِ الرَّجُلِ وَيَشُقُّ خَلْعُهُ أَكْثَرَ وَحَاجَتُهَا إِلَيْهِ أَشَدُّ مِنَ الْخُفَّيْنِ
1/266 شرح العمدة لابن تيمية