The skin may feel stiff to the touch, but the tissue under is still warm and soft. There is very little chance of blistering, infection or permanent scarring as long as it is treated properly. The skin will be white or blue and will feel hard and frozen. 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.