What is the origin of the phrase "I need to see a man about a horse"?

[BJMoose]

@Surok

That’s the one I know, as well, so perhaps we can assume that’s the British variant. And someone, when it crossed the pond, the dog mutated into a horse.

The floridated water did it.

[John_Mace]

@FRDE

I’ve never heard it about a horse

• but ‘I need to see a man about a dog’ is familiar.

From the first cite in the second post:

The variations on these expressions are endless and include: Go see a dog about a horse, go and see a dog about a man, go and shoot a dog, go and feed a dog…