American Northeast proof: layers, as other posters have said. My strategy is, from bottom to top: sneakers (I don't have boots at the moment), thick socks, long underwear or pajama bottoms, pants, T-shirt, sweater or sweatshirt, waterproof winter jacket, balaclava, beanie or other warm and flexible hat, hood over the hat. This is enough to get you through the coldest day of the year almost everywhere people live, but since I mostly walk between heated building, this lets me strip down to long pants and a T-shirt if I need to.