The phrase “one horse town” is American; we use the expression disparagingly to designate a town of such limited resources, so sleepy and dole-so, that one horse might be able to do all its necessary transportation.
The usage first reported (1855) credits the expression to New Orleans, but as it was reported a few years later as far north as Boston, a place notably reluctant to accept new terms, it is more than likely that it had come into wide popular use quite a long while before it appeared in print.