أَوْ خَافَ الْجُنُبُ إِنِ اغْتَسَلَ بِالْمَاءِ يَقْتُلُهُ الْبَرْدُ أَوْ يُمْرِضُهُ، فَإِنَّهُ يَتَيَمَّمُ بِالصَّعِيدِ
Meaning: Or a person requiring a full bath fears that bathing with water in severe cold will kill or make them ill; then the person may perform tayammum with pure earth.
The excuse concerns credible danger to life or health, not ordinary discomfort from cold water.