What are the specifications of socks upon which one is permitted to wipe, and is it a condition that they be made of leather?

It is permissible to wipe over socks (khuffs) and shoes (na'layn), and this is indicated by the hadith of Mughirah ibn Shu'bah, which Al-Albani authenticated. A sock (jawrab) is defined as a foot covering made of wool for warmth. Ibn 'Umar said: "Wiping over socks is like wiping over leather slippers (khuffayn)." Ibn Hazm permitted wiping over anything worn on the feet above the ankles, whether it be a khuff or a jawrab made of any material, whether leather or non-leather.