I htink of armies in chariots, not regular commercial traffic. Riding horseback would be preferable, IMO.
Now I need to look up chariot pictures....
http://new.tigtail.org/TIG/TVM/E/Ancient/Greek/Greek-art/0_precursers/frescos/M/mycenae_women_chariot_with_ladies-tiryns.c12cbc.jpg
http://www.dnmartgroup.com/images/Artwork/Roman%20Chariot.jpg
http://www.eleganza.com/detailed/pix/chariot.jpg
I believe I'd prefer a chaise with netting and pillows conveyed by some lackeys with a very smooth gait.