Blood transports nutrients and oxygen to muscles. Blood carries carbon dioxide, lactic acid, and other waste products away. Water helps excrete waste products from your body. Water transports heat from the muscles to the skin. Sweat cools the body.
Water helps to moisten and warm cold air before it hits the lungs.
Body fluids help to maintain skin temperature in cold weather. You've waited too long. Thirst is your body's signal that it's already dehydrated. It is not proportionate to what your body needs. In fact, the body may suppress thirst during exercise.