I say, and with God's success: It is not permissible, and it is necessary to remove the socks, as wearing them then does not lift the impurity of the feet; due to the failure to meet the condition of wiping: which is wearing the socks while in a state of complete purity at the time of the event after wearing them, unlike if one completes the ablution before a nullifier occurs; as narrated by Abu Bakrah : "Indeed, he  permitted for the traveler three days and their nights, and for the resident a day and a night, if he purifies himself and wears his socks, he may wipe over them," in Sahih Ibn Khuzaymah 1: 96, and Sunan al-Bayhaqi al-Kabir 1: 281, and Sunan al-Daraqutni 1: 204, and Musnad al-Bazzar 9: 90. Refer to: Bada'i al-Sana'i 1: 9, and the commentary of al-Tahawi on al-Maraqi p. 129, and God knows best.