A pony is a glass of only 140 ml capacity sometimes known as a small beer. The name comes from the old horse race carnivals, where patrons would go to the bar for a quick drink between races. Because only a short amount of time was available between races many patrons would prefer to drink beer from the small 140 ml glass (4.7 U.S. oz.) so that they would be done in time to get back to the next race. While a pony is a small horse, not commonly used in racing, the name stuck nonetheless.
Alternately, a pony glass is a small, stemmed glass containing approximately one ounce or more of liquid. The origin of the name "pony" is obscure, though the related names of "cordial glass" and "liqueur glass" derive from this vessel's typical usage for liqueurs.