I've often pondered over that phrase, and it didn't make much sense to me, considering how it was used (not here). Logically thinking, if someone's mouth is so cold that it wouldn't melt butter, that would mean they're a pretty cold person. So, I finally looked it up. This is what Merriam-Webster says.
Definition of butter wouldn't melt in someone's mouth
chiefly British
—used to say that a person who appears to be innocent, sincere, or kind is really not
Is that what you meant? Some of the other instances where I've seen it used gave the impression that it meant the opposite of what M-W says.