How on earth do you get hypothermia while backpacking!?!! Sweaty and smelly I get. Insect-devoured, sure.
Jumping jacks? Done that. Thought that is a harsh way to warm up when really cold.
If there is dry, clean ground available, there is nothing like push ups to warm up quickly. Otherwise, a brisk hike is the best in my experience. If my partner and I have the entire run or runs to ourselves, I plan the fishing so I break it up with walks.
I must share genes with Thor Heyerdahl who in his older age and wisdom retired to Italy. My hands get cold very quickly.
I suffer Reynaud Syndrome which can be really painful when your digits turn pasty white. A 5 kilo chrome bright steelhead carefully released in 2,5 celsius water may be a joyful moment but the pain is still very real.
I tried butane powered hand warmers but they kept going out. So if the daytime air temperature is not forecast to go over 5C (41F), I wimp out, stay at home, perhaps go cross-country skiing where I am more than comfortable down to -15C (5F).
In addition to wool or fleece finger mitts, a thick wool Andes-style toque that covers the ears and back of the neck seems to help me the best.
Science is not common sense. Much of it is devoted to a systematic documentation of what we do not know and understand.