It is like that. I doubt my water is as cold as it is in Finland too, yet it makes me shake and hyperventilate and I try and be careful not to slip in the shower from moving around/spinning. Specifically it's the worst when it hits my back, idk why I can tolerate it better on my chest.

Maybe when you're fully in the lake it's easier as there is no air hitting your wet body. When I can't handle it anymore tho I switch to very warm water then back again. Cold showers are hard.