Was "a horse of a different color" a common phrase around the time of The Wizard of Oz?

Another variant: “That’s a horse of a different feather.”

Not one I’ve ever heard. Not disputing you; thanks for the interesting data point.

Exactly. Taking the phrase literally is the joke, and it joke works because the phrase was well-known.

That’s a reply to “birds of a feather flock together” when you disagree with it. Similar to “apples vs oranges”.

Well, that’s an orange of a different… Wait.

If an orange is of a different color, is it still an orange?

Ripe oranges are often green.

You don’t have to be familiar with horses to use idioms with horses in them, any more than you have to be a mariner in the era of sailing ships to use the hundreds of nautical phrases which have become part of the English idiom, such as at the helm, run a tight ship, loose cannon, the devil to pay, all hands on deck, get on board, sailing close to the wind, batten down the hatches, etc.

Or all the agricultural words and phrases that you might not even recognize as related to farming: broadcasting, reaping what you sow, etc.

Without checking, I’m fairly sure the Marx Brothers used it as a sight gag, probably in A Day at the Races, which was released in 1937.

Wasn’t that a B&W flick?

Well, How Green Was My Valley and The Scarlet Empress were both B&W.

Yeah, it is a B&W film. That wouldn’t rule it out completely though and I really can’t think where I saw the scene if it wasn’t there.
Three people are talking in the foreground as several dark coloured racehorses are led past in the background. A much lighter coloured horse appears and Groucho remarks out of the blue, ‘now, that’ s a horse of a different colour’