What is the ruling on someone who has a wet dream twice in one night, when the night was cold and rainy, and he performed ghusl the first time, then had a wet dream a second time? Is he obligated to perform ghusl again within a short period?

You must perform ghusl again for the second wet dream that occurred after performing ghusl and prayer. The occurrence of two wet dreams in one night does not matter. However, if the second wet dream occurred before ghusl, then one ghusl suffices. You can heat water, apply oil, and stay in a warm place to avoid the harms of cold.