My view is a bit more pragmatic....
I used to don ever thicker layers of neoprene to survive in the sea.... and still my hands would go pasty white and lose all feeling and function.
Then I read about this guy and thought, never mind the theories, he does actually swim in water with literal chunks of ice floating about in it, so ok, lets try it.
And yup, it works. I now swim in ordinary trunks and my hands go a beet red and carry on working.
So what's my theory?
Dead simple. I have a big log of fuel (overweight with a big tummy) I just need to get it burning well. ie. Get the bellows going and get it burning.
Toss in this bit of plain observational science... https://en.wikipedia.org/wiki/Nasal_cycle
ie. Your nostrils can and do change size.
My guess is the "breathe lots and then hold your breathe" triggers the nostrils to expand so it's easier to breathe lots.
Is there any more to it? I don't know don't care. I just know I feel better after one of these cold swims.
Weird. But true.
In retrospect, I'm not surprised that such a facility exists within humans. After all, many other animals survive in cold conditions, early indigenous tribes did and still do.