I have very cold fingers 1week after carpal tunnel release surgery. is this normal?

No, but possible --: Due to these reasons: 1: with tight splint or bandages, your fingers maybe bluish in color, tingly or cold; 2: with hand held hanging down most of the time ; bandages, the circulation in fingers is not great; 3: if you are not exercising your fingers or are or have been a smoker, then fingers do feel cold. 4: some people have cold fingers for no specific reason, with nothing to do with surgery.

Not really: If you already had very cold fingers before surgery, then this may not be a problem. But if this has occurred since the surgery, then you need to go back to your Doctor for an evaluation.