There is a foot ointment that contains cayenne pepper in it that can do the same thing as just plain cayenne but, it's not as bad when you're in a body comfortable situation, your feet don't burn they just keep a little warmer than usual. I use it to treat the neuropathy of my feet and it does keep them warm but they don't burn. I can't find my tube so I don't know the name but, I believe you can find it at most drugstores.
One technique I use while hunting in very cold weather is to put one of those hand warmer packets inside each of my boots alongside my ankles. On top of the socks not against my skin. My whole body stays warm even when I'm out hunting in teen temperatures. There is a larger concentration of blood vessels in your feet/ankles than the rest of your body and with this, if you apply heat in that area, your whole body will be warmed as there is that larger concentration of blood vessels to carry the heat to the rest of you.

This seemed as good a place as any to insert this - I used to have an old Ford Fairmont that was horrendous for freezing my feet as I made my routine travels over the mountain passes between Eastern and Western Washington. A ski fanatic friend suggested I try a spoon full of cayenne in my socks. I figured, "why not." At worst the laundry lady would beat me for turning my socks red. Well, I tried it and it works. My trip over the passes was the first in ages in which I suffered no discomfort from the cold. The discomfort came later - as I waited, for over six hours, at SeaTac Airport for my sister (she missed her flight twice). I had to go into the bathroom two times to wash the cayenne off the soles of my feet. I had been quite comfortable outside in the snowy cold, even though I was in casual shoes, but being inside was another story.

The short of it is, in addition to other reasons that are or will be set out in the sections relating to health matters, cayenne should be included in your emergency kit. It truly will keep your feet warm. A word of caution though, stay with the store bought type (e.g., Safeway, Albertsons, etc.). They tend to be somewhat mild and in my one experiment proved adequate for the cause. I don't known what would happen if I threw some of my 180 btu stuff in my socks. I probably couldn't walk on snow, since it would likely melt.

I don't know the actual medical or scientific details about this phenomenon. It bears further looking into. I do not know if it would protect your feet from frostbite or if the heat is just a result of sensation. I suspect there is some effect aside from sensation, since the cayenne would increase circulation and thus heat transfer from the body to the feet.