Is it permissible to wipe over cloth socks, and what is the scholarly disagreement regarding this issue?

It is not correct to absolutely state that wiping over a cloth sock is impermissible; the issue involves detail. The Hanbalis held the view that it is permissible to wipe over a sock if it is thick and one can continue walking in it. Ibn Qudamah narrated from seven or eight Companions the permissibility of wiping over socks. Al-Tirmidhi said that the hadith (definition) of Al-Mughirah ibn Shu'bah regarding the Prophet, peace and blessings be upon him, wiping over his socks and sandals is "hasan (definition) sahih (definition)" (good and authentic). As for Abu Hanifa, Malik, Al-Awza'i, and Al-Shafi'i, they do not permit wiping over them unless they are also sandals. Sheikh al-Islam Ibn Taymiyyah held the view that it is permissible to wipe over a sock even if it does not stay on by itself but by a string or similar means. However, a thin sock that reveals the skin cannot be wiped over, according to the correct position within the Hanbali madhhab (definition).