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A ludicrous cavalcade, in ridicule of a man beaten by his wife. It consists of a man riding behind a woman, with his face to the horse’s tail, holding a distaff in his hand, at which he seems to work, the woman all the while beating him with a ladle; a smock displayed on a staff is carried before them as an emblematical standard, denoting female superiority: they are accompanied by what is called the ROUGH MUSIC, that is, frying-pans, bulls horns, marrow-bones and cleavers, &c. A procession of this kind is admirably described by Butler in his Hudibras. He rode private, i.e. was a private trooper.
Definition taken from The 1811 Dictionary of the Vulgar Tongue, originally by Francis Grose.
Riding St * Riff RaffNathan Bailey's 1736 Dictionary of canting and thieving slang
John S. Farmer's collection of canting songs and slang rhymes
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Francis Grose was independently wealthy, having inherited money from his father, a jeweller. Finding himself overspending, he published a number of books; his Provincial Glossary seems to have been the starting-point for the Vulgar Tongue reproduced here.