It's just damaging your body, and putting you in very real danger of dying. Yes, that can shock you into starving off depression, and when your body is in that life or death mode, you're not going to have a flu. That doesn't prove anything, especially if you don't adhere to the conventional view of disease and the immune system being opposites, rather than symbionts.
Could paleo people in cold weather areas manage to swim in super cold water and survive? I'm sure they could, if they really needed to. But your body tells you not to do it for a reason. Leave the icy swim to the polar bears, the penguins, the seals and the walruses, all of which have evolved means to insulate their body heat from the freezing cold water.
