In response to cold your body causes blood supply to the skin to drop in the whole body. This is to conserve heat, but results in us feeling really cold. Exercising reverses this, resulting in an increased blood supply to the skin in order to remove excess heat and in this case we feel hot.
As mentioned, the head receives a large blood supply, and continues to do so despite other tissues being restricted. This is particularly as a result of the brain requiring a lot of oxygen and glucose. This keeps our head warm.
This phenomenon is why hats keep us warm and are important in cold weather, we lose a lot of heat from our head.
It is also likely that the skin on our head contains less cold receptors, as these aren't likely to be required. However the other parts of our body, particularly the soles of our feet and anterior surface of our hands have many sensory receptors. They are likely to make first contact with anything that may be harmfully cold.