My wife has the same exact problem, her left index finger is alot colder then the rest! It is always the same finger and she puts it on the side of my neck or face so i can see that she is not crazy, lol. She also has some pain running down her thumb into her wrist. The Doctor today said it's the hand you use every day so it is probably just hurting and gave her some anti inflamatory pills! (what a joke) he never heard about a cold finger.
After reading this she did have back surgery 10 months ago and she did have pressure on her nerve in her back giving her sciatica down her leg. She also has had diabetes in her family. She is very fit and we are hoping it is poor circulation or something with her nerve and maybe some adjustments might help! Thanks to all that responded!