During Prohibition in the United States, the phrase see a man about a horse was most commonly used in relation to the consumption or purchase of alcoholic beverages.
While reinforced by both of these examples:
"Any general business that needs attending to that you may not care to discuss whith the present party.
We can meet for lunch on Tuesday, since I'll be in the area; I have to see an man about a horse.
by moth17 Jul 5, 2005"
"2. see a man about a horse 271 up, 73 down"
A discreet way to leave the table at a restaurant to go to the restroom; derived from a 1940's black-and-white film (sorry, cannot recall the name) where an actor literally says it as he leaves a table to see a man at another table about a horse.
"Excuse me, I have to see a man about a horse."
The origins date back to the days of the "Not-Quite-So-Wild-Yet-Still-Wild Enough Old West". When at the local drinking establishment (read at the Saloon) the horse trough was closer to the entrance of the building (usually directly attached) than the outhouses which were generally situated out back. And thus a slang term was born. And of course MOST people had enough common decency to only use the trough for number one.