In the US, the first one would be okay - and this reply would only be appropriate between very good friends, or family members, or between a husband and wife, or boyfriend and girlfriend. The second one is not used in the US, even between close friends or family members. It sounds way too intimate even for a husband and wife.
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Anonymous It sounds way too intimate even for a husband and wife. In fact, it sounds downright creepy; you might hear something like this in a horror movie."Let me touch your hand" is "too intimate even for a husband and wife" and "creepy"??? I would agree that it's not a very natural response to "my hands are cold," but I don't find it nearly as alarming a