The tissue underneath is still undamaged. Blistering is likely which is why medical treatment should be sought out. Proper treatment is critical to prevent severe or permanent injuries. The tissue underneath is hard and cold to the touch. This is a life threatening injury.
Deep frostbite needs to be treated by a trained medical professional.
The tissue underneath has been damaged, in severe cases amputation may be the final recourse to prevent severe infection. Blistering will happen. Proper medical treatment in a medical facility with personnel trained to deal with severe frostbite injuries is required to aid in the prevention of severe or permanent injury. When you are exposed to cold with the extremities including your feet, hands, nose, ears, and face being at the highest risk, the blood vessels constrict. This is a natural reaction to prevent body heat loss and hypothermia.