Cauterization = using heat to sear your skin shut.
Cayenne pepper does have hemostatic properties though, they use on stomach ulcers- just mix cayenne pepper and water into a thick sludge, and convince the patient to drink it.
I’ve never heard about using it on your feet, though, is that to increase circulation? When hiking in the winter, I have warm feet right up until I stop moving, and they don’t get warm again until I change socks and crawl into my sleeping bag, so thats interesting to me. How cold is really cold? 20F? 0F? -40F?