My baby always has really cold hands is this normal?  

Depends. Babies, like adults, can have cold extremities simply because of the environment. Cyanosis, or a blueish color, to the fingers or hands can be a little more concerning - though not always. I wouldn't be too concerned unless there is consistent cyanosis or a curious change/decrease in finger/hand movement. Use mittens and if you're really concerned, talk with your doctor.