Tayammum may also be performed out of fear of the cold.
ʿAmr ibn al-ʿĀṣ related: “During the expedition of Dhāt al-Salāsil I had a nocturnal emission on a bitterly cold night. I was afraid that if I bathed I would perish, so I performed tayammum and led my companions in the dawn prayer. They later mentioned this to the Prophet ﷺ, who said, ‘O ʿAmr, did you lead your companions in prayer while you were junub?’ I explained what had prevented me from washing and added, ‘I heard Allah say: “Do not kill yourselves; indeed Allah is ever Merciful to you” (al-Nisāʾ 4:29).’ The Messenger of Allah ﷺ laughed and said nothing.”
Abū Dāwūd and others transmitted the report in both a disconnected and a connected form; both versions are authentic, and al-Ḥāfiẓ declared it sound in Fatḥ al-Bārī. We have discussed it in detail in Naqd al-Tāj, no. 45.
If the water on hand is not enough for both wuḍūʾ and ghusl, one should use it to wash the limbs in the proper order, then perform tayammum for whatever remains, because the Prophet ﷺ said, “When I command you to do something, do of it as much as you can” (agreed upon). This is also the position of Ibn Ḥazm (2/137).
20 – The manner of performing tayammum
ʿAmmār reported: “I became junub but could not find water, so I rolled in the soil and prayed. I then told the Prophet ﷺ what I had done. He said, ‘It would have been enough for you to do like this,’ struck the ground with his palms, blew on them, and then wiped his face and hands.” (Agreed upon)
Thus tayammum consists of a single strike for the face and the hands; this was the view of Aḥmad, Isḥāq, and others.
As for wiping the entire arms, there is no proof for it (al-Muḥallā, 2/156–158).