It sounds like raynaud's disease to me. It's not really anything to worry about. Try to avoid the cold exposure by wearing warm clothes and gloves.
http://www.mayoclinic.com/health/raynauds-disease/DS00433
I hope this helped
Hi, I also get extremely cold as well. I'm 16. In the winter my fingers swell up to 1 inch big and they turn bluish purple. This could be because your daughter has bad circulation- I do, or it could be a reaction to certain weather types of food. I always go purple in winter or the cold.