I did that once. Pro tip, if you ever consider it: wear as little clothing as possible. Your skin instantly goes numb and you can't feel your water-logged clothing, which makes for a dangerous situation. Get a pair of water shoes or crocks or something that secures to your feet, no socks, tight shorts, no shirt. Have a towel nearby and dry clothes.
The day I did it was January 1st, the air temperature was like 28F and the water temperature was 33F. I wore too much clothing, but overall it wasn't that bad.
I strongly suspect I'll never do it.
They often cheat and use a portable sauna. They'll sit in there for a while and then go take their dip. Another one is sauna and then roll in the snow.
I just can't bring myself to be quite that insane!
When I was younger, we'd go out on the ice and stomp on it until we broke through. We'd then walk back with our pants freezing solid. We were not bright children and I'm still sometimes baffled that we reached adulthood.
They have a 'Polar Bear Club' that chops a hole in the ice and then takes a dip.
I've not yet been intoxicated enough to even consider that an option. (And I've been pretty damned wasted!)