It may be because your skin is very dry and irritated. It could be an allergic reaction to a lotion or soap you are using. It could also be a form of dermatitis that a doctor could diagnose.
If you've been out in the cold, a minor frostbite can kill the outer layer of skin, causing it to slough off. This can happen even if you've worn gloves, if you were out too long.
Your fingers could be peeling as a result of a recent skin infection or rash that resulted in you having dry skin. Dry skin is the most recognised cause of peeling skin as well as sunburn.
