Is it permissible to delay performing ghusl and re-performing the prayer for someone who had a wet dream and fears the cold weather and illness, or is it obligatory to hasten it?

If you remember after performing ablution (wudu') and prayer (salat) that you were in a state of major ritual impurity (janabah), you must perform a ritual bath (ghusl) and repeat the prayer. If you fear harm from cold water, you must heat it or warm the place. If you are unable to heat the water or fear an increase in illness, you may perform dry ablution (tayammum) and pray immediately, then perform ghusl when the fear subsides. Nocturnal emission (ihtilam) alone does not necessitate ghusl unless you are certain that semen has been discharged.