In the US we usually think of Standardbreds as harness racing horses. But here and in other parts of the world the Standardbred and similar breeds are also raced under saddle. The US Trotting Association has an interesting article about the hows and whys of under saddle racing here.
Here's a video of such a race in France:
Prix du Cornulier 2006
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One interesting feature of under saddle racing is that many of the riders are women. This has been true historically, too. The famous Standardbred Greyhound broke a record back in 1940 with a woman riding.
And more recently the speedy mare Moni Maker broke that record, with jockey Julie Krone riding.
A nice little 10 minute documentary tells the story of Moni Maker's achievement, with footage of historic races, an interview with Julie Krone, and Moni Makers record breaking trot.
Part 1 is here.
Part 2 is here.