cold water is invigorating and if you need a little bravery to jump into a cold shower, then the feeling of accomplishment (you have conquered something) that follows is pleasant. So there are a physiological response plus a psychological satisfaction working in concert. At any rate, I think kaliope mentioned that, do whatever makes you feel the way you want to feel at a given moment, even if the mechanism of why it helps is hidden from you.

You probably know it, but just in case let me mention this - Korean steambaths, Finnish saunas, etc. all require that you drink lots of tea in the process. Otherwise they are not safe for you.