Why are horns included in woodwind quintets?

There is a genre of classical chamber music written for groups known as woodwind quintet (or wind quintet). A quintet is composed of five instruments: a flute, an oboe, a bassoon, a clarinet, and a horn. The first four in this list are all woodwinds, so why is the horn (a brass instrument) included in these groups?
Since the heyday of classical music when wind ensembles were most popular, horns have always performed together with woodwinds. When it comes to other brass instruments, the trumpet has long been a noble instrument associated with the court and the military, and the trombone has been seen as a sacred instrument for performing at churches. The horn has been the only brass instrument within reach of the common people, making it easier for them to enjoy. Since wind ensembles first took shape in an age where there was no clear sense of any distinction between woodwinds and brass, and at some point along the way the group came to be called a woodwind quintet.
(Reference: Compendium of Interesting Wind Instrument Facts, Yamaha Music Media)