This was interesting. Someone asked Tom Skilling, the longtime meteorologist at WGN in Chicago what exactly was a Buttermilk Sky?

His answer: The song that you refer to, "Old Buttermilk Sky," was written by Hoagy Carmichael and Jack Brooks in 1946 for the movie "Canyon Passage" and was actually nominated for an Oscar. The phrase "buttermilk sky" refers to a sky that is peppered with patches of midlevel altocumulus clouds or high-level cirrocumulus clouds that tend to take on a globular appearance similar to the texture of cultured milk. These clouds are more commonly referred to as forming a "mackerel sky," especially when the cloud elements line up in rows resembling the scales or spots of that fish. A mackerel sky is often an indication of the presence of high-level atmospheric moisture and instability and may portend thunderstorms.

http://articles.chicagotribune.com/2005-02-27/news/0502270205_1_wgn-clouds-hoagy-carmichael