Is it permissible for a teacher who suffers from extreme sensitivity to cold and water to pray without ablution during cold times?

A Muslim must pray with proper purity. If he is able to perform ablution by heating water or washing his limbs gradually while covering them to avoid harm, he is obliged to do so. However, if he fears harm and cannot avert it, he should resort to Tayammum (definition) by striking pure earth once for his face and hands. This is the view of the majority of scholars. The evidence for this is the Almighty’s saying: "And do not kill yourselves," and "And do not throw yourselves with your own hands into destruction," as well as the action of Amr ibn al-Aas and the Prophet Muhammad’s (peace be upon him) confirmation of it. This reflects the ease of Islamic law and the removal of hardship, confirming the Almighty’s saying: "And He has not placed upon you in the religion any difficulty."