Please don’t try to be condescending, it rarely works and will just leave you sat there looking small and stupid...
I would draw your attention to this British Medical Journal article which quotes the US Army study...
Festive medical myths -- Vreeman and Carroll 337: a2769 -- BMJ ... its a very well documented study, so I’m a little surprised you aren’t aware of it? The original US Army study is referenced in the article, so you can probably find it.
The human body regulates its own temperature and loses heat evenly from the skin, and does not lose 80 to 90 percent of heat from the ends. The head, hands and feet make up around 20% of the surface area of the body, so would have to lose heat at around 4 or 5 times faster than other areas... I’d be interested in seeing the research you took this from as it contradicts all the medical information I’m aware of?
The cold injuries you’re referring to will be due to cryogenic insult to the cells in the body due to the formation of ice crystals inside them, or possibly due to anoxia due to the closing of blood vessels. When exposed to extreme cold the body limits blood flow to surface vessels to limit heatloss. This can cause lack of oxygen to outer regions, which can cause damage to tissue but most damage is caused by the formation of ice crysals. These can cause damage to the cells by rupturing them but also by changing the amount of water in the cells which can lead to higher pH levels, changes to proteins. I can direct you to some very good pathology text books which would help with this.
Hyperhidrosis is primarily caused by an imbalance in the hyperthalamus and physical conditions such as temperature sadly have little to do with it. It would be much more easy to treat if it were down to physical conditions...