The principle of relaxation in case of ibadah (worship category) is based on principle of usar (‘ghair mamoli mushaqqat’ / ‘undue difficulty‘) and for other prohibitions (‘mohramat’/’things which have been declared Haram’), the relaxation is based on iztiraar (becoming impossible to do or when it becomes a matter of life and death). More can be listened to in the following response of Ghamidi Sahab:
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Since Ghusal and Wuzu belong to ibadah category, therefore, to avail any relaxation in this regard, principle of usar will apply. In winters, considering the level of difficulty and basing on the directive of Tayammum in Quran, Prophet Muhammad (sws) allowed Masah over socks which are worn after performing complete Wuzu (for 24 hours). Therefore, in order to perform Masah on other body parts, the level of ‘usar’ (‘ghair mamoli mushaqqat’ / ‘undue difficulty’) should increase as compared to the one that was originally necessitating masah over socks. Same goes for Tayammum, difficulty that one is facing is something that cannot be countered with Masah anymore.
Please see for further details:
Discussion 31457