The Circus Historical Society is a great organization for those interested in the details of circus history. Their website has excellent research resources, and the organization holds an annual convention. Many members specialize in particular areas of circus history, and some are active in modern circuses.
There are some interesting articles on the site (about all aspects of circus history, not just horses). One discusses earlier styles of horse act, including dramas acted out by people on horseback, or "scenic" riders who posed in costume to depict famous characters or well-known scenes from myth and legend while standing on horseback. Later, fast-paced action became more appealing to audiences than these earlier forms.
This Wiki page has a small collection of photos of circus horse acts, both modern and historic. Many of the photos are old ones from the German federal archive.
The poster shown above is from the New York Public library digital archives. Click on it to visit the original page and see a larger version.