wagonette

noun, a four-wheeled horse-drawn pleasure vehicle, open or with a removable cover, with facing seats along the sides and one or two seats arranged crosswise in the front (COD)

“The wagonette, we use it quite a bit for weddings that want the whole party to go.”

“I have a Cinderella Carriage, three vis-a-vis, a landau, and a wagonette.”