Heat Transfer from our Bodies

It happens via phase change. Water (or sweat) must absorb energy from its surroundings to change to a vapor. This energy is called "latent heat". So, water that is on your skin and in your lungs evaporates, taking some thermal energy with it while the temperature does not actually change. Thus, if the air is dry enough, vapor containing thermal energy is taken away from your body and dissipated to the air. This feels oh-so good in the summer time.

note: A person WILL heat up the air around them, just ask an HVAC guy about that.

And dont forget that in fear, your body contracts the veins reducing the amount of blood circulating in non essencial areas. This also contributes to the cold skin feeling, as well as the palid look.