Cold air does not steal your warmth; physics does, through predictable heat transfer. A winter coat keeps you warm not by generating energy, but by slowing the escape of thermal energy your metabolism produces every moment.
The human body runs continuous metabolic reactions that release thermal energy, often described as basal metabolic rate. Without protection, that heat flows outward by thermal conduction into surrounding air, and by convection as moving air currents carry warmed air away from your skin. A well-designed coat adds insulation: layers of fibers create tiny pockets of still air, which has low thermal conductivity. By reducing air movement inside the fabric structure, the coat cuts convective heat loss as well.
Heat also leaves the body as infrared radiation. Many modern fabrics use reflective linings that bounce part of that radiation back toward the body, reducing net radiative loss without creating any new heat. All three pathways—conduction, convection, and radiation—are governed by thermodynamic gradients. The coat simply narrows those gradients around you, so the same body heat that would rapidly disperse into cold air instead accumulates in a thin, warmer microclimate next to your skin.