What could be wrong if you sweat just sitting in a cold room?

It depends on a lot of things. If you are 38 years and up you could have the start of peri menopause (yes, it is true that SOME women go through their peri menopause for several years at earlier ages.) You could be nervous. Pinched nerve in the body. Poor circulation. Exercising will heat you up and you'll sweat even when it's cold. Running a fever. If it keeps up & there is no simple explanation, please see your doctor.