Only reason I turn the cold knob to the left is when someone else in the house drops the pressure and I need to avoid looking like a lobster, or when the pressure is so low having come through the hot cycle that I need the pressure to hose stuff off me.
I have taken completely cold showers, one time it was on a camp site when I woke up at 4am and did not know what the time was. It was not pleasant.
I take showers to get clean. Cooling off in the UK at least amounts to go stand in the shade for 5 minutes with a drink, which can be a hot one if you like such things.