Can he do tayammum on intensely cold days in the case of janaabah?
Question

Can I pray after doing tayammum in the case of janabah on intensely cold days, knowing that I do not have the ability to purify myself immediately? In addition to that, I get ill because of the cold that affects my back, which affects me a great deal.
Praise be to Allah.The person who becomes junub and wants to pray must wash himself with water, because of the verse in which Allaah says (interpretation of the meaning): 
“If you are in a state of Janaaba (i.e. after a sexual discharge), purify yourselves (bathe your whole body)”
[al-Maa’idah 5:6]
But if a person is unable to use water because there is none available, or it is available but using it will make his sickness worse, or because it is very cold – and he has no means of heating it – then he may do tayammum with dust instead of doing ghusl with water, because Allaah says (interpretation of the meaning): 
“But if you are ill or on a journey, or any of you comes after answering the call of nature, or you have been in contact with women (i.e. sexual intercourse), and you find no water, then perform Tayammum with clean earth”
[al-Maa’idah 5:6]
The verse indicates that a sick person who will be harmed by using water, such as if doing ghusl will lead to his dying or his sickness getting worse, or his recovery being delayed, should do tayammum. Allaah has told us how to do tayammum, as He says:  
“and rub therewith your faces and hands”
[al-Maa'idah 5:6]
And Allaah has told us the reason for this law, as He says (interpretation of the meaning):
“Allaah does not want to place you in difficulty, but He wants to purify you, and to complete His Favour to you that you may be thankful”
[al-Maa'idah 5:6]
It was narrated that ‘Amr ibn al-‘Aas (may Allaah be pleased with him) said: I experienced a wet dream on a cold night during the campaign of Dhaat al-Salaasil, and I was afraid that if I did ghusl I would die, so I did tayammum, then I prayed Fajr with my companions. They mentioned that to the Prophet (peace and blessings of Allaah be upon him) and he said: “O ‘Amr, did you lead your companions in prayer when you were junub?” I told him what had kept me from doing ghusl and I said: “I heard Allaah says (interpretation of the meaning): ‘And do not kill yourselves (nor kill one another). Surely, Allaah is Most Merciful to you’ [al-Nisa’ 4:29].” The Messenger of Allaah (peace and blessings of Allaah be upon him) smiled and did not say anything. 
Narrated by Abu Dawood, 334; classed as saheeh by al-Albaani in Saheeh Abi Dawood. 
Al-Haafiz ibn Hajar (may Allaah have mercy on him) said: 
This hadeeth indicates that it is permissible for the one who thinks that using water will kill him to do tayammum, whether that is because of cold or some other reason, and it is permissible for the one who has done tayammum to pray with those who have done wudoo’. 
Fath al-Baari, 1/454 
Shaykh ‘Abd al-‘Azeez ibn Baaz (may Allaah have mercy on him) said:  
If you can find warm water or you are able to heat the cold water, or you can buy water from your neighbour or from someone else, then you must use that, because Allaah says (interpretation of the meaning): “So keep your duty to Allaah and fear Him as much as you can” [al-Taghaabun 64:16]. You have to do whatever you can, whether buying the water, heating it or whatever ways will enable you to do wudoo’ as prescribed with water. If you are unable to do that and the cold is severe and is posing a danger to you, and there is no way for you to heat it or to buy some warm water from those who are around you, then you are excused, and tayammum is sufficient for you, because Allaah says (interpretation of the meaning): 
“So keep your duty to Allaah and fear Him as much as you can”
[al-Taghaabun 64:16]
and: 
“and you find no water, then perform Tayammum with clean earth and rub therewith your faces and hands”
[al-Maa’idah 5:6]
The one who is unable to use water comes under the same ruling as one who cannot find any water. 
Majmoo’ Fataawa Ibn Baaz, 10/199,200 
You have to wash whatever you can of your body, such as washing the hands, feet and so on, so long as that will not cause you any harm, then do tayammum. 
We ask Allaah to grant you a speedy recovery, and to make what has befallen you an expiation for your sins and cause you to rise in status. 
And Allaah knows best.