Hittites
Technically horses & carriages have never ended. The Amish and Mennonites and still use them. And, you can still pay for a ride in them in Manhattan's Central Park. In the general culture there is no point where they suddenly ended, they just grew less and less commonly used after the mass production of cars. They pretty much faded away in the 1940's.
This depends on the type of carriage used. A three horse hitch is often called a unicorn hitch or a three up hitch. In Russia a carriage desined for three horses is a Troika.
The horse-drawn carriage was still in use in the early 1950's, even though the automobile has been around since the turn of the century. I remember the ice wagon bringing ice for our icebox (non-electric refrigerator) each day in a horse-drawn wagon in 1953. I live in an area of Missouri heavily populated by Mennonite familys, so I see horse-drawn wagons nearly every day in my home town.
Tom Thumb
Horse drawn vehicles have been thought to have been present all throughout human history, sometimes refered to as Carriages. The same is true of "Kings." Both have a history long predating the 1500's.
A Russian horse carriage with three horses harnessed abreast is called a Troika. The two outside horses are bent slightly to the outside and must canter to keep up with the center horse which is harnessed straight in and trots.
A cart.
Answer 2:
A two wheeled vehicle pulled by a horse could be a cart or a sulky.
A two-wheeled vehicle, beginning with a "c", that is pulled by a horse could be a chariot.
There are several:
A horse-drawn carriage with a folding top could be a landau.
* sled * sleigh is probably the one
* sledge * toboggan skibob
The proper, traditional term is a "Coachman", which applies to the driver of any kind of horse drawn carriage.
The Horse Drawn Chariot was invented in the year 1,700 B.C.E.
A 20-mule team, which was actually 18 mules and 2 horses in the lead, could pull 10 tons of coal or borax ore.
No one invented horses pulling cars. This came about out of necessity. Early automobiles were notoriously unreliable and would commonly break down requiring them to be pulled by a horse.
Typically a horse drawn wheeled battle vehicle would be called a chariot or a battle wagon.