All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
Prayer has a magnified status in Islam, as it is the second of its pillars and Allah, the Exalted, ordered to maintain it when He said (what means): {Maintain with care the [obligatory] prayers and [in particular] the middle prayer and stand before Allah, devoutly obedient} [Quran 2:238]. The severe threat against one missing it and underestimating it has been established, as Allah, the Exalted, said (what means): {But there came after them successors who neglected prayer and pursued desires; so they are going to meet evil.} [Quran 19:59], and He, the Exalted, says (what means): {So woe to those who pray, [but] who are heedless of their prayer.} [Quran 107:4-5]
You must utilize any means possible to perform Ghusl [bathing] for Janabah and to establish the prayer at its time. We advise you with these following points:
1. Make the water warm so that there is no coldness.
2. Bathe in a warm place.
3. Stay inside the place you are bathing in until your body is dry.
4. Use oils after bathing.
5. Do not expose yourself to cold air after bathing.
If you take care of these issues, then you will never find any excuse of "harm" from the use of water, if Allah, the Exalted, wills. We alert you to beware of the whispers of satan as he might whisper to you that you could become ill due to Ghusl, but this is not true. Such is only a trick of satan to invalidate the most important of obligatory acts of worship upon the Muslim, which is the prayer.
However, if after taking these steps you are vulnerable to an illness, or an increase in it, or a delay in its cure, then in such a case you are permitted to perform Tayammum [dry ablution using clean earth to enter a state of purity], and the prayer is not to be neglected as long as one's intellect is intact except in two cases: menstruation and post-partum bleeding.
The evidence for this is what Abu Dawood and Ahmad narrated from ‘Amr ibn Al-‘As, that he said:
I had a wet dream one cold night during the That As-Salasil Expedition (against Persia). I feared that I would die (from the cold), so I performed Tayammum and then led my companions in the morning prayer. They mentioned that to the Prophet, sallallaahu ‘alayhi wa sallam, and he said: "O ‘Amr! You led your companions in prayer while you were Junub?" I then told him about what prevented me from washing and said, "I heard Allah saying: {And do not kill yourselves [or one another]. Indeed, Allah is to you ever Merciful.} [Quran 4:29]" The Messenger of Allah, sallallaahu ‘alayhi wa sallam, then laughed (in approval) and did not say anything.
Allah knows best.