If you are traveling with a procession of people on horseback, you are part of a cavalcade.
The word cavalcade comes from the Latin word for horse, caballus. The word cavalry, which means soldiers on horseback, comes from the same Latin root. So strictly speaking, a cavalcade is group of people on horseback or in horse-drawn carriages, moving together in some kind of ceremony or parade. But cavalcades can include vehicles or people walking, like the motorcycle cavalcades that sometimes accompany a funeral procession.
