In the Name of Allah, Most Gracious, Most Merciful.
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Wiping over socks while performing ablution is a general dispensation given to Muslims; it has not to do only with the winter. It is permissible to wipe over the socks throughout the year for travelers and residents as well.
In his response to your question, Dr. Husam al-Din Ibn Musa `Afana, professor of principles of Islamic jurisprudence at Al-Quds University, Palestine, states the following:
According to the majority of scholars, wiping over socks is a general dispensation given to Muslims during ablution. There are various hadiths reported in this regard. It is reported on the authority of Thawban (may Allah be pleased with him) to the effect that the Prophet (peace and blessings be upon him) dispatched a garrison to some destination; its soldiers got cold. When they returned and complained to the Prophet (peace and blessings be upon him) about this, he (peace and blessings be upon him) advised them to “wipe over their head covers and foot covers too.” “Foot covers” applies to socks and any covering used to protect feet against cold, etc.
It is also reported on the authority of Al-Mughirah ibn Shu`bah that "The Prophet (peace and blessing be upon him) performed ablution and wiped over his socks and slippers" (Ahmad, Abu Dawud, At-Tirmidhi, and Ibn Majah).
There are other hadiths which refer to the fact that the Prophet performed ablution and wiped over his socks and slippers.
Wiping over socks was also reported to have been practiced by some of the Prophet's Companions. Ibn Al-Mundhir said, “Nine of the Prophet's Companions were reported to have wiped over their socks; these are `Ali, `Ammar, Abu Mas`ud Al-Ansari, Anas, Ibn `Umar, Al-Bara’, Bilal, `Abdullah ibn Abu Awfa, and Sahl ibn Sa`d.” Abu Dawud also mentioned some other Companions as having wiped over their socks, too. Those are Abu Umamah, `Amr ibn Huraith, `Umar, and Ibn `Abbas. The fact that there are thirteen of the Prophet's Companions reported to have wiped over their socks proves that they did so out of following in the footsteps of the Prophet (peace and blessings be upon him), for they would not do so on their own.
It is to be noted here that wiping over socks is a general dispensation that is not peculiar to the season of winter as some people think. It is permissible any time throughout the year for travelers as well as for residents. But there is a duration of wiping to be stuck to by residents and travelers. The residents are allowed to wipe over their socks for one day and night, while the travelers are allowed to wipe over them for three days and nights.
Also keep in mind that there are certain conditions for wiping over the socks: first, the person is to put them on while in a state of purity. Second, the duration of wiping begins after nullifying ablution after putting on the socks.? For example, if one has made ablution for the Fajr Prayer and put on his socks, and then his ablution is nullified, the duration of wiping over the socks in his case starts from the time he makes ablution for the Zhuhr Prayer of this day until the time of the Zhuhr Prayer of the following day if he is resident, or the Zhuhr Prayer of the third following day if he is a traveler. This is the most dependable opinion given on this point. If the duration of wiping finishes before one has nullified ablution, the ablution is still valid because the completion of the duration of wiping is not a nullifier of ablution.
You can also read:
How to Wipe over Socks in Wudu’
Rules for Wiping over Socks in Wudu’
Suffering from Eczema: Can I Wipe over the Socks?
If you have any further questions, please don't hesitate to write back!
May Allah guide you to the straight path, and guide you to that which pleases Him, Amen.