بسم الله الرحمن الرحيم
(Fatwa: 149/151/N=02/1435)
All the authentic and reliable mujtahideen and scholars of fiqh agree that it is not lawful to do masah (wiping) over cotton or woollen socks which filters water, or which cannot stand on shank without tying due to its thickness, or ones with which it is not possible to walk 1-2 miles.
کما فی بدائع الصنائع (1:83 ط زکریا دیوبند): واما المسح علی الجوربین ۔۔۔ فان کانا رقیقین یشفان الماء لا یجوز المسح علیھما بالاجماع اھ
و فی البحر الرائق (1:318 ط زکریا دیوبند): وفی المجتبی: لایجوز المسح علی الجورب الرقیق من غزل او شعر بلا خلاف اھ
Therefore, it is not lawful what some brother do masah over traditional cotton or woolen socks. Such a masah is invalid, and wudhu will not be invalid in case of invalidity of masah. Thus, they perform salah without wudhu. (For details see: Fatawa Usmani 1:368-379)
Allah knows Best!
Darul Ifta,
Darul Uloom Deoband