Reference: http://www.alfawzan.af.org.sa/node/15905
Question: Whoever wakes up on a cold day [and finds himself] in a state of janaabah, can he do tayammum [instead of having a bath]?
Response: If he fears [harm] for himself, and has nothing with which to heat up the water, then he should do tayammum, because Allaah ‘Jalla wa ‘Alaa said:
{And do not kill yourselves [or one another]}, Soorah an-Nisaa, Aayah 29
And [it has been reported that] whilst in battle, ‘Amr ibn al-’Aas woke up one cold night in a state of janaabah, and did tayammum, and thereafter prayed with his companions. So when he returned [from battle], he mentioned this [incident] to the Prophet ﷺ, and the Prophet ﷺ approved of [him having done] that.
