According to This is Finland, the correct way to enjoy the steam is “to take off all your clothes and… sit, naked, with others for a while and sweat. Then you will go outside and jump (still naked) through a small hole in the ice on a lake, the sea or whatever and refresh yourselves in the freezing water—or roll in the snow instead.” This hot and cold back-and-forth might seem crazy, but not to Finns. A few rounds of plunging into near-freezing waters than retreating into near-boiling air is believed to be the perfect remedy to a night of heavy boozing.
Toi be honest, I don’t do the hole inthe ice or the snow thing. But a cool shower is pretty refreshing when your body temp has gone up. The rise is body temp is largely on the skin (not your innards).
Any cause to worry? I have heard that folks with heart problems might want to keep the temperature changes minor, but aside from that, I think you are good to go!
BTW, I would moderate the boozing in the sauna. Replacing water with booze can be a bit shocking!