It is not permissible for a man who is in ihram to wear socks but it is permissible for a woman. If a man in ihram needs to wear them he has to offer the ransom. The late Sheikh Ibn `Uthaymeen, a prominent Saudi Muslim scholar (may Allah shower mercy on his soul), states that: It is not permissible for men to wear socks in a state of ihram. However, there is nothing wrong if a woman wears socks. If a man in ihram needs to wear socks because of sickness, it is permissible for him, but he has to offer the ransom, which is either to sacrifice a sheep or to feed six poor persons or to fast for three days. He may do whichever of these three he wants.
Allah Almighty knows best.