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 of Al-Mughirah ibn Shu'bah regarding the Prophet, peace and blessings be upon him, wiping over his socks and sandals is "hasan sahih" (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.