Hi Rachel
DD used to get blue hands from the cold. Not sure if it's as blue as your DD, but I was pretty concerned about it to. I asked the Dr when we went for a check up and he said not to worry, that is was just the cold, just more noticable because of her pale skin. If your DD's skin pinked up when she warmed up it's probably the same thing, but if your concern ask the Dr.
HTH