The warming sensation is called "hunter reflex" and is usually well developed in animals that regularly come into contact with cold temperatures. Like the feet of Antartic (and Artic for that matter) birds who wade for fish and even many Sherpa and Eskimo tribes. Your Hypothalmus (part of the brain) senses the drop in temperature and restricts blood to that area in a move to keep from losing a lot of heat from that location in the body. At the same time it tells your frontal lobe, "get the fuck out of the cold water/snow/etc you dip shit." If you don't follow that command it will compromise by alternating between constricted vessels and dilated vessels to keep some heat flowing, but minimizing the heat loss through that area. By the time this happens, usually the victim has added lots of clothes and ends up overheating. Their brain, in it's altered state, responds by removing clothes. The Hypothalmus though, gets fed up, and being well beyond hypothermia, it decides that losing the limb is worth overall survival.