Answer
(Fatwa: 1063/1063=J)
If you wear leather socks (or socks on which Shariah allowed to do masah) in state of wuzu then you can do masah (wiping wet hands over) in the specified period, there is no need to wash the legs. The specified period of masah for a muqeem (one who is at home not in journey) is one day and night, and for musafir (one who is in journey of more than 48 miles) is three days and nights.
(2) It not permitted to do masah on cotton socks.
قال النبی صلی اللہ علیہ وسلم: یمسح المقیم علی الخفین یوماً و لیلۃً والمسافر ثلاثۃ ایام و لیالیھا، رواہ البخاری عن عمر فی باب المسح علی الخفین 1/58، وفی البدائع: فان کانا رثیقین یشفان الماء لا یجوز المسح علیھما بالاجماع۔
Allah (Subhana Wa Ta’ala) knows Best
Darul Ifta,
Darul Uloom Deoband