First of all, it should be clear that the Shari`ah specifies that the top of the sock is to be wiped.
In his well-known book, Fiqh As-Sunnah, the late Sheikh Sayyed Sabiq states:
“The Shari`ah prescribes that the top of the sock is to be wiped. Al-Mughirah narrated: “I saw the Messenger of Allah (peace and blessings be upon him) wipe over the top of his socks.” (Reported by Ahmad, Abu Dawud and At-Tirmidhi)
`Ali Ibn Abi Talib (may Allah be pleased with him) observed: If religion (Islam) was based on one’s own reason, the bottom of socks would take precedence in being wiped over the top of socks. (Reported by Abu Dawud and Ad-Daraqutni)”
Dr. Muzammil H. Siddiqi, former President of the Islamic Society of North America, states: “It is permissible to wipe over the socks whether they are made of leather or some other material. So many Prophetic hadiths state that the Prophet (peace and blessings be upon him) wiped over khuffayn or the leather socks and jawrabaiyn or light socks.
Al-Mughirah Ibn Shu`bah said: “I was in the company of Allah’s Messenger (peace and blessings be upon him) on one of the journeys and he went out to answer the call of nature (and after he finished) I poured water and he performed ablution; he washed his face, forearms and passed his wet hand over his head and over the khuffayn.”
The socks must cover the whole foot including the ankles. The rule is that one should make full ablution and then one should put on the socks. One can wipe over the socks if one has put them on first time after ablution.
After that the wiping over them can be done for five prayers for those who are not traveling. The traveler is allowed to wipe over the socks for three days and nights as long as he/she keeps them on.
Wiping can also be done over the shoes if they are full like socks and cover the ankles. Also one has to keep them on like socks if one wants to wipe over them.
It is not allowed to wipe over the shoes that we normally wear, because they do not cover the ankles and we take them off at the time of prayer.”