I'll elaborate on what's already been said.

First of all: Butter will melt in anybody's mouth--eventually. If the person is alive and kickin', butter will melt in anybody's mouth.

But the expression is an exaggeration to make a point. The person in question is so very cold, unsociable, frigid that butter, a very melting substance in warm mouths, won't melt in her mouth (even though we know that since she's alive butter actually would melt).

As a child, the expression confused me. I heard my mom apply it to someone in our neighborhood. I puzzled and puzzled over the expression. I thought to myself, "But butter will melt in her mouth! And yet my mother says it wouldn't melt in her mouth. Why? Why? Why!!! This doesn't make any sense. Why is it that butter won't melt in her mouth? What is it about her mouth that keeps butter from melting? I know my mom wouldn't lie to me. I think my mom is incorrect. Butter MUST melt in her mouth! I need to take a close look at her mouth...." And so on. Eventually the real meaning of the phrase hit me later on in life. Oh, what a sense of relief I felt! I melted!