Praise be to Allah.
The scholars differed concerning the ruling on a woman wiping over her head cover; there are three views:
The majority – which was also narrated from Ahmad – are of the view that it is not permissible for her to wipe over it only, and they ruled that if she does that, her wudoo’ is invalid, unless the head cover is thin and the water can penetrate it.
In al-Mudawwanah (1/124) it says:
Maalik said concerning a woman wiping over her head cover: She had to repeat her wudoo’ and her prayer. End quote.
We should point out here that ash-Shaafa‘i (may Allah have mercy on him) said that the permissibility of wiping over the head cover depends on whether the report that mentions it is saheeh. There are some saheeh reports concerning that, such as the hadeeth of Bilaal in Saheeh Muslim (275), according to which the Messenger of Allah (blessings and peace of Allah be upon him) wiped over his khuffayn (leather socks) and head cover. So ash-Shaafa‘i (may Allah have mercy on him) should be included among those who allow wiping over the head covers of both men and women.
The Hanbalis, according to the other report from their imam, are of the view that it is permissible to wipe (over the head cover) and the wudoo’ is valid. This is also the view of Ibn Hazm, who said:
Anything that is worn on the head, such as a head cover, cap, helmet and chain-mail, and so on, it is permissible to wipe over it, and women and men are the same in that regard, whether there is a reason to do so or not.
A third group are of the view that a distinction should be made between that which is difficult to remove and that which is easy. In the first case they regard it as permissible to wipe over it, but not in the second case. This is the view of Ibn Taymiyah and, among contemporary scholars, Shaykh al-‘Uthaymeen.
Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said:
With regard to a woman wiping over her head cover, there are two reports:
According to the first report it is not permissible, because the texts that speak of the concession only refer to men for sure, whereas there is some doubt as to whether they refer to women.
According to the second report, it is permissible, and this is the apparent meaning of the general words “wipe over the khuffayn and the head cover.” – Narrated by Ahmad (39/325). The commentators said: The hadeeth that says that the Prophet (blessings and peace of Allah be upon him) did that is saheeh, but the hadeeth that says he allowed it is not saheeh, and women are also included in that, along with men, just as they are included with regard to wiping over the khuffayn…
And because it is permissible for men to wipe over the head cover, so that is permissible for women too, like men. And because it is clothing that it is permissible to wear on the head and it is usually difficult to take it off, so it is likened to a man’s head cover, and more so, because the woman’s head cover covers more than the man’s head cover, and it is more difficult to take it off, so the woman's need for (this concession) is greater than in the case of the khuffayn.
Sharh al-‘Umdah, 1/265, 266
Shaykh al-‘Uthaymeen (may Allah have mercy on him) said:
Whatever the case, if there is some difficulty, either because it is cold or because it is difficult to take it off and put it on again, then there is nothing wrong with being lenient in matters such as this, otherwise it is better not to wipe over it, as there is no saheeh text concerning this matter.
Ash-Sharh al-Mumti‘ ‘ala Zaad al-Mustaqni‘, 1/239
The third view is the one that is most likely to be correct. It is proven from the Prophet (blessings and peace of Allah be upon him) that he wiped over his head cover, and there is no difference between the head cover of a man and that of a woman; in fact it is more appropriate that this should be permissible in the case of women, because of the reasons mentioned by Shaykh al-Islam.
Based on that, not every head covering may be wiped over; rather if the head is covered with something that might be problematic to take off, as in the case of a woman who fears that her hair may be seen, or she has covered her head to which she has applied henna, or it is very cold and she fears some harm (if she takes off her head cover), and other similar excuses.
See also the answer to question no. 139719
And Allah knows best.