This phrase means that someone is being prim and proper with a cool kind of demeanour. But from what event or phenomenon or occurrence was this idiom derived from, and when?
It goes on to say,
Eric Partridge offers this citation in A Dictionary of Slang and Unconventional English:
So, onward to cheese, we find — nothing useful. Partridge is curiously silent on the subject, at least as it relates to this case directly. I wonder if his reticence might be due to one unsavory meaning of the word, use of cheese for smegma, giving the whole thing a lewd sexual connotation. But I can find nothing in the O.E.D. or elsewhere to support this contention. Still, if cheese is somehow related to butter in this context, this could well shed a whole new light on that phrase as well. But given the lack of sources, I have to conclude this is a dead end.
Still, we might also consider another meaning of butter as "fulsome flattery, unctuous praise" (Partridge). A young woman who was demure, as Partridge calls it, would be likely to receive much of this kind of butter.
A woman who was "reserved, modest, and shy" would probably seem a little cold, and certainly resistant to the kind of buttering flattery that might come her way.