Praise be to Allah.
It was narrated that al-Mugheerah ibn Shu’bah said: “The Prophet (peace and blessings of Allaah be upon him) did wudoo’ and wiped over his socks and shoes.” (Narrated by al-Tirmidhi, 92; classed as saheeh by al-Albaani in Saheeh Sunan al-Tirmidhi, no. 86)
The author of al-Qaamoos said: jawrab (socks) means something that is wrapped around the feet.
Abu Bakr ibn al-‘Arabi said: jawrab means a thin cover for the feet made of wool, worn to keep the feet warm.
It was narrated that Yahyaa al-Bakka’ said: I heard Ibn ‘Umar saying, “Wiping over the socks (jawrabayn) is like wiping over the leather slippers (khuffayn).”
Al-Musannaf by Ibn Abi Shaybah, 1/173
Ibn Hazm said: wiping over anything that is worn on the feet – of things that are permitted to be worn and which come up above the ankles – is Sunnah, whether they are slippers (khuffayn) made of leather or felt or wood, or socks made of linen, wool, cotton, camel hair or goat hair, whether leather is worn over them or not, or whether they are overshoes or slippers worn over slippers or socks worn over socks.
Some scholars differed as to whether it is permissible to wipe over the slippers (khuffaayn). The correct view as indicated by the evidence is that it is permissible to do that, as stated above.
And Allaah knows best.
See the answer to Question No. 8186 and 9640