I douse everyday (initially not for IS purposes, but for health purposes--yes..I got it from those crazy Russians while I was doing Systema lol) and I found that after every douse I had a greater awareness of the "skin" under the skin.
In Systema, the focus is always on breath because it is pretty much the gateway to relaxation (at least psychological relaxation..but I'm thinking it has physical effect as well--I know for sure that if you douse properly, you will heat up your body like a mini-fever so that the heating of this body will try to kill the sick cells in your body) so when we pour very cold water on ourselves, we "resist" the inclination to tense up by breathing (albeit, not by reverse breathing or by any other form of "yogic" breathing..just a simple exhale through the mouth).
Perhaps we relax the outer layer of the body (i.e., the muscles) so that we engage the fascia which might have ...uhmm...heating properties or contains a system that increases blood flow and heat in the body (all you rolfers and myofascial release and acupuncture peeps help me out here!) to warm the body to counterbalance the cold. Kinda like the IS teacher telling you to relax your muscles against incoming force so that you can contract the fascia to let that manage the incoming forces.
Since I do this everyday, Ill explore it tonight when I take a shower. And the dynamics you are laying out here for cold water dousing is giving me ideas on how breath (and not even necessarily reverse breathing) affects the contraction of fascia and perhaps how Systema's insistence on relaxation through breath could be tapping into aspects of IS training.
I have no problem with breath training, IS training, or cold water misogi, but. . .
I find this post so full of assumption that I would recommend long and intense periods of contemplation before you comment any further on this subject.
First off, I'm not at all sure that breath is the "gateway" to psychological relaxation. And it is quite clear that we are psycho-physical beings, so anything psychological will necessarily have a physical effect.