Near here where I live the local University has a parade every fall but they won't let horses participate. Something to do with insurance and clean-up.
When I was growing up I rode in the local town parade and rodeo every year, it was alot of fun. They don't do it anymore. The little town is now a good sized city with alot of traffic. Don't suppose it would be feasible to shut down the highway for a parade. And the city arena was torn down for a playground.
We have horses in the Nevada Day Parade here, although the numbers are decreasing. Horses also play a big part in any of the small town parades for the Fourth, Christmas, etc. We are hoping to get our ranch in the next Nevada Day parade as an entry, or as part of the Horseman's Assoc. entry. Parade just has to have horses :)