Is it sufficient to remove the traces of semen and perform tayammum to pray after a wet dream, or is ghusl obligatory if the weather is cold?

If a Muslim is unable to perform ghusl (ritual bath) due to illness or severe cold, and cannot find anything to warm the water, then he should perform tayammum (dry ablution) and does not need to repeat (the prayer); this is based on the Almighty's saying: ﴿Allah does not burden a soul beyond its capacity﴾ [Al-Baqarah: 286], and on the action of Amr ibn al-Aas and the Prophet's (peace be upon him) approval of it.