It wasn't blue, was it? As long as you feel pain, it should be okay. You just froze your skin, a stage of frostbite, but nothing you won't recover from. Bad frostbite is when you completely lose blood flow, and the flesh turns blue or black. That represents a time when you should go to the hospital, and you'll most likely lose your frozen finger.
Don't use warm water to warm up any frozen flesh. Always start with cool water, and gradually warm up as the feeling returns. The warm water will shock the flesh and nerves, and cause more damage than was already there.
EDIT: Oh, and it would be best to try and protect your pinky from the cold until it feels better and your blood vessels are fully dialated again (until blood flow is normal). Right now it will be painful because freezing damage was done. Your body cuts off it's blood supply to cold appendages in order to maintain your core temperature at normal. That is why you get numb in the extremities after being out in the cold for awhile. Take it from a guy who has fallen through the ice of a frozen pond.