What is a Charette?
The term “charette” evolved from a pre-1900 exercise at the Ecole des Beaux Arts in France. Architectural students were given a design problem to solve within an allotted time. When that time was up, the students would rush their drawings from the studio to the Ecole in a cart called a charrette. Students often jumped in the cart to finish drawings on the way. The term evolved to refer to the intense design exercise itself. Today it refers to a creative process akin to visual brainstorming that is used by design professionals to develop solutions to a design problem within a limited timeframe.
www.library.cmu.edu/Research/ ArchArch/Charette/what.html

I would go for "chariot"

Estilo Chariot (Charrete Romana) Ideal para 2 pessoas Tamanho: 170x147cm 4 pegas acolchoadas Superfície em Nylon reforçado Válvula tipo Boston. ...
www.filipemotoshow.com/loja/details.clab?cPath=22& products_id=44&PHPSESSID=a147081f37232b44fc5e53...

O site http://www.bbno.freeserve.co.uk/carriages_glossary_waggon.ht... tem uma série de definições para veículos puxados por cavalos. Entre os vários de duas rodas, creio que o termo charrete equivale a cabriolet ou gig. Cart, apesar de ter duas rodas, não corresponde às charretes que conheci. Pelo menos aqui onde eu moro, a charete (ainda vi algumas na infância) é um veículo para transporte de passageiros. Assim, eu acho que cabriolet ou gig são mais apropriados que cart. Eis as definições para os três termos, retiradas do site acima:

Cabriolet
A light, two-wheeled, hooded one-horse chaise. Replaced the curricle as a fashionable vehicle for society men in the early years of Queen Victoria's reign

Cart
A two wheeled waggon with the advantage of being more manoeuvrable, suitable for hilly districts and drawn by only one horse rather than a team. A general-purpose trade or farm vehicle with no suspension. Special versions had a tipping mechanism and were often used for carting manure (dung carts) or building materials.

Gig
A light two-wheeled, one-horsed vehicle for two people. Used by commuters, it was the most common vehicle on the road. See a real Kinross Square Gig and a Cab Fronted Gig here.

I'd probably translate it as carriage, however it would depend specially on the context as well as on the type of vehicle. A carriage, acording to Wikipedia, is a "four-wheeled horse drawn private passenger vehicle with leaf springs (elliptical springs in the 19th century)"; if this is the approximately the context, I would definitely go with this one