Literally frostbite is the term that is used to describe an area of tissue with that has lost the ability to function due to not having much blood flow due to to a extreme low in temperature. If you begin rubbing a frostbitten section you could of course exaggerate the severity of the wound by breaking the fragile area and forming wounds to which bacteria enter. Additionally you could start influencing blood flow into the area which could then start the process of gangrene (decay), which could bring toxic byproduct of the decay into the body, which could begin shutting down your body starting from the kidneys... A common disease from something like this is rhabdomylosis.
