Geese stand on one leg to help regulate their body temperatures. This stance is used in an attempt to help the geese conserve as much body heat as possible.
Like other birds, a goose does not have warm feathers covering its legs. This lack of insulation in the lower extremities causes a decrease in body temperature. A goose lifting one foot allows the lifted leg to be closer to the bird's central body heat and warm feathers, which causes the body temperature to bump back up. This one-legged stance is rotated between legs, so each appendage has an opportunity to keep warm.