In the early days, every car was a convertible.
Seriously. Just look at this early car ad from 1898, from the Winton Motor Carriage Company, one of the first manufacturers that sold cars in the United States.
The name says it all: they didn't make cars: they made carriages. They simply replaced the horse with a "hydrocarbon motor", promising "no odor". That last bit makes sense if you remember that, while you have to sit behind the horse and get to experience whatever comes out of it, the motor exhaust can be directed behind you where it brings pollution to everybody else on the road.