The original 18th century standard English use of one-horse meant ‘drawn or worked, by a single horse’. By the mid-19th century it had gained wider, metaphorical use.
“ ’One horse’ is an agricultural phrase, applied to anything small or insignificant, or to any inconsiderable or contemptible person: as a ‘one-horse town,’ a ‘one- horse bank,’ a ‘one-horse hotel,’ a ‘one-horse lawyer’ “, explained Charles Dickens in his magazine, All the Year Round (1871).
One of the earliest recorded uses comes in a poem ‘The One-Horse Town’, written by A. B. Ufferer, published in Graham’s Illustrated Magazine (Philadelphia, PA, Volume 53, Page 178) included the following chorus.
…In a mean little, green little one-horse town,
Sing pizzerinctum high!
Sing doldelorum low!
Oh would I could draw a lottery prize
And pack up my trunk and go!