Today the search for horses in Rome takes us to the National Museum of Oriental Art. This museum is an interesting collection of Eastern artefacts from the Middle East to Japan, ancient to modern, and many addenda to the collection because of Italian archeological exploration. You can find many interesting representations of horses. These are just a few.
The Museo Nazionale d'Arte Orientale is not far from the main train station in Rome, Stazione Termini. Via Meruluna, 248.