Charioting refers to the act of riding on a chariot or a similar vehicle. However, there are various synonyms that can be used in place of this word. For instance, you can use the term "carting" to describe the act of riding on a cart. Additionally, "wagoning" can be used to describe the act of riding on a wagon. Essentially, "charioteering" can also be used to mean the same thing. If you are looking for a more colloquial term, you can use "riding on a chariot" as it's easy to understand and less technical. Regardless of the synonym you choose, they all imply riding on a vehicle that's pulled by one or more animals.