Some people take the notion of mechanical horses much more literally than as a metaphor for a motorcycle or car. here are some examples of modes of transport with one horsepower.... I am listing only horses that actually make forward motion with a rider or drawing a carriage.
While many have imagined mechanical horses, including patents filed in 1878 and 1893, few constructed a version that actually worked.
1932: Sam Barton's Horse
Sam Barton was a Vaudeville clown who liked to entertain the crowds with his bicycle powered horse named Dobbin.
Sam Barton was a trick bicyclist on the music hall stages, and this horse was an extension of this act, that he took out onto the public streets.
1933: Horse of Steel
This Italian petrol-engine powered horse had mechanical steel pipe legs. It was said to be able to traverse relatively rough terrain. However it is hard to imagine the 5-horsepower motor supporting much in the way of speed.
Observers report it more closely resembled a grasshopper than a horse. The creator, Alzetta planned to create a higher horsepower model, but it does not seem that this ever came to pass.
1930s: Bouncing Horse
This toy turns up and down motion into forward progress--albeit rather slowly. It comes in many different sizes and designs. A modern example is shown below.
1941: Roy Sheldon Gas Powered Horse
This model had a slight galloping motion although the legs seem to have been fixed in place.
1951: Bogart's Mini-Horse
George A. Bogart created a small mechanical horse that could pull a cart on level ground with good traction.
W.J. McIntyre created a series of horses where a petrol engine turned small wheels under the hooves. The legs moved but the motion was cosmetic rather than locomotive.
1988: Ricky and Pete
Ricky and Pete was a movie that featured a mechanical horse.
2004: Movie Prop Horse
This one is in on a bit of the technicality....
Not exactly a horse, but the four-legged RT is equipped for a comfortable ride.
2009: Maker Faire
This mechanical horse appeared at the Maker Faire in Newcastle. I am not sure that it really meets my requirements of forward motion and ride-ability, but I am giving it the benefit of the doubt.
2012: Steampunk Robot Horse
Links to other mechanical horse pages:
At this point the desire to create a mechanical horse seems to be more aesthetic rather than practical. That is to say, it looks cool but does not make a lot of sense. However as processing power and robotics expertise improves artificial equines may become a more "real world" option for covering difficult terrain unsuitable for wheeled vehicles.