Is it permissible for one in a state of major ritual impurity (junub) to pray with tayammum (dry ablution) in intensely cold weather, while ill, and unable to perform ghusl (full ritual bath)?

One must perform ghusl (ritual bathing) with water to purify oneself from ritual impurity (janabah). However, if the use of water is not possible due to its unavailability, or if its use would cause harm, such as illness or severe cold, then tayammum (dry ablution) with earth is permissible as a substitute, by wiping the face and hands. This includes those who cannot find warm water, or cannot heat cold water, or cannot afford to buy it. If it is possible to wash some parts of the body without harm, then those parts must be washed, and tayammum performed for the remainder.