I was asked, "If a girl says her hands are cold, does that mean I'm supposed to hold them?"

I would say no, BUT I think the guy should ask, "Do you want me to hold them for you?" Chances are, if she's not attracted to you, it will freak her out if you just grab her hands. Unless you're 100% positive that she likes you / is attracted to you (and who is 100% sure??), then you could hold her hands and keep them warm. I think you're better off asking. :)