Wearing socks in ihraam for men and women
It is not permissible for a man who is in ihraam to wear socks, but it is permissible for a woman to do that.
Shaykh Ibn ‘Uthaymeen said in al-Sharh al-Mumti’ (7/154): Question: is it haraam for her (i.e., the woman in ihraam) to wear socks?
The answer is no. Socks are haraam for men (in ihraam).
If a man in ihraam needs to wear socks, it is permissible for him to wear them, but he has to offer the fidyah (ransom), which is either to sacrifice a sheep, or to feed six poor persons, or to fast for three days; he may do whichever he wants of these three.
The Standing Committee was asked: what is the ruling on wearing socks on the feet and doing tawaaf al-qudoom in them during Hajj, and doing the tawaaf of ‘Umrah in them during ‘Umrah?
They replied:
It is not permissible for men to wear socks when in ihraam for Hajj or ‘Umrah. If he needs to wear them because of sickness etc, then he must offer a ransom (fidyah), which is to fast for three days, or to feed six poor persons, giving each one half a saa’ of dates or similar food, or to sacrifice a sheep.
Fataawa al-Lajnah al-Daa’imah li’l-Buhooth al-‘Ilmiyyah wa’l-Ifta’, 11/183.