Go on a spree, usually drinking and dancing, but can refer to other activities.
According to the Handybook of Literary Curiosities, by William S. Walsh (Lippincott 1892), the expression is American slang meaning to go on a reckless debauch, to be wildly extravagant. Originally, the metaphor applied to bonfires painting the sky or scenery red. An old Irish ballad contains the lines:
The beacon hills were painted red
With many a fire that night.
The phrase was helped into popularity by the fact that `to paint’ (ie to paint the nose red) was an old slang term for drinking.
Another suggestion is an English source, a tale from 1837, when the Marquis of Waterford and a group of friends ran riot in the town of Melton Mowbray, painting the town’s toll-bar and several buildings red. This source is plausible, but the phrase isn’t recorded in print until fifty years after the Marquis enjoyed his night out.
In America, the first use of the phrase in print was in the July 1883 issue of The New York Times:
“Mr. James Hennessy offered a resolution that the entire body proceed forthwith to Newark and get drunk… Then the Democrats charged upon the street cars, and being wafted into Newark proceeded, to use their own metaphor, to ‘paint the town red’.”
Another theory is put forward by William and Mary Morris in their Morris Dictionary of Word and Phrase Origins. They link it to the American frontier and to ‘red light district’ and suggest that people out for a night ‘on the town’ might very well take it into their heads to make the whole town red.
We’ll never know who first coined the phrase, or whether his nose was red when he did so. But of all the possible sources, I like the Irish ballad best.