The walker's body will do three things to help slow the decrease in core body temperature. The first is the walker will begin to shiver. Shivering is the spasming of muscles, the muscles as they work generate heat, through respiration, this heat helps to reduce the rate of temperature decrease.
Secondly the muscles at the root of the hairs on the arms and legs of the walker will contract, causing the hairs to stand on end. This is known as goosebumps. The hair will then trap a thin layer of insulating air, helping to slow the heat loss to the environment.
Thirdly the blood vessels in the extremities of the body, such as the hands and feet, will constrict. This is known as vasoconstriction, and this means that less blood is near the skin and so there is less heat loss to the environment.