What is the ruling when someone experiences a wet dream before Fajr, performs tayammum, prays Fajr, and doesn't make Ghusl due to cold weather? Is this acceptable?

As for what has already happened, he has to repeat the two prayers which he prayed without performing Ghusl from Janābah (major sexual impurity). (This is) because he is in the city, and he can heat the water and make Ghusl with it. As for the issue itself: If a man wakes up while he is in a state of major sexual impurity, and he fears the cold and doesn’t have anything to heat [the water] with, then he performs tayammum [dry ablution]. However, if it [i.e., the water] becomes warm or he finds something to heat it with, it’s obligatory for him to make Ghusl. And if he is traveling on land and has water, but it is cold, and he doesn’t have something to heat it with, then, in this case, it is permissible for him to perform tayammum from this Janābah (major sexual impurity). And if he is capable of using water that doesn’t harm him, it becomes mandatory for him to perform Ghusl.