What is a four wheeled horse drawn carriage with open seat at the front for driver?

A four wheeled horse drawn carriage can have many different styles and names, just like a car. A horse drawn "carriage" is simply a four-wheeled, horse drawn conveyance...a two wheeled conveyance is called a "cart". You start to differentiate between a four wheeled "carriage" and a "wagon" by it's uses. Although certain styles of horse drawn "wagons" can also be considered a carriage, such as a wagonette or a hotel wagon, you would not necessarily call a delivery wagon, such as a hitch or express wagon, a "carriage".

Like cars, many carriages were given names by their manufacturers that then stuck with other manufacturers (think "Coupe", for example, which originated with carriages). A coach, which is an enclosed carriage, was either made as a hard top (always enclosed), or an "auto-top", meaning the top could be folded down in good weather (like a convertible). Carriages that can never be enclosed, such as a Victoria, are never called "coaches".