Does freezing your skin reduce pain?

If you're in your doctor's office and he sprays a little freon on the injection site to numb the skin, that does in fact reduce pain. But it doesnt FREEZE the skin. Freezing the skin is frostbite. It's often disfiguring and a heck of a way to lose toes. The difference is that, with the spray, it may even allow frost to form but nothing really gets frozen.