I don't think you can compare cold showers indoors with winter swimming in a lake.
Water from the tap may not be that pure but it'll definitely freeze solid somewhere around 0°C. Water from the lake is salty, so it's got a lower freezing point & is most likely below 0°C during winter. Worse, as soon as you get out of the water, you'll have to face the freezing cold wind (even colder than the water) against your wet skin.
Good luck!
I wouldn't do it for the health benefits (I do ok with a glass of orange juice every morning). I'd do it for the sake of adding one more thing to my list of "crazy things you've done in your life".
