According to [1] what I find interesting is:
> In contrast, in trained individuals, practicing the learned breathing techniques resulted in an immediate and profound decrease of pCO2 and bicarbonate, and an increase in pH (reaching up to 7.75 in individual subjects; Fig. 2 and Movie S2), indicating acute respiratory alkalosis.
I'm not a doctor, but since I was part of the study and asked them a lot of questions, I can sort of interpret what they found, which is that your CO2 levels drop (among other things).
With the WHM breathing technique that means you'll be getting into a territory of prolonged oxygen deprivation. In my case I'd be holding my breath for 3 minutes (while completely breathing out beforehand, without the WHM, I could only hold my breath for 20 seconds).
They measured that while doing the WHM your adrenaline level is on average higher than your peak adrenaline level while you're bungee jumping.
> Epinephrine levels in trained individuals were even higher than those reported in a recent study in which acute stress elicited by a bungee jump was found to suppress cytokine production by leukocytes ex vivo stimulated with LPS (13).
It might be in the article, but my suspicion is that this is because of prolonged oxygen deprivation. See also Fig 3A for how high the adrenaline levels got.
So to me it's clear that the WHM gives you a lot of adrenaline. What does adrenaline do? Well, it makes you numb, it acts as a painkiller in the sense that it makes you feel less (again not a doctor, but based on my limited knowledge this is a fact). So that's one reason why it's easier to jump into really cold water.
Moreover, it yields some evidence to some "mind over body" claims. It isn't really mind over body, it's adrenaline that can be conjured consciously at will. I'm speaking also from personal experience [1].
[1] I've done this at many Dutch dance festivals (e.g. Liquicity, Mysteryland). Instead of taking drugs, I'd do the WHM to spike my adrenaline levels as high as possible and had a great time.