It might just be normal for her. It was for my younger cousin. However, sweating with cold clammy skin can also be side effects of thyroid problems and diabetes.
While I am sure she is probably fine, it wouldn't hurt to give the pediatrician a call and let him know what is going on. He may have other questions that can rule out thyroid or diabetes problem or he may order some blood work just to be sure.
One thing you didn't mention is whether or not the house is air conditioned or uses fans, what the temperature of the house is or other things that could be affecting her. Like I said though, the best thing would probably be to call the pediatrician and tell him what she is doing (the sweating) and any other things that seem a little abnormal and just double check to make sure he doesn't think it warrants further investigation. Please don't hesitate to call them. Most offices are happy to take your call even if it seems like a silly question. Sometimes the things that seem just like they are strange quirks with us can actually be symptoms of something. Sometimes, they are just the way we are.
Good luck. Hope this helps.