As far as I know the Romans did not use a specific breed of horse for their racing. The race team owners bought their horses from specific breeders, who bred the animals for speed and endurance. Matched teams were also in demand. I don't think that they even had named breeds of horses such as our Thoroughbreds, Tennessee Walkers, or Appaloosas.
The Quadriga races.
they would have a track and horse drawn chariots
The chariot races were held at a race track called circus. In the eastern part of the Roman Empire they used the Greek name: hippodrome.
A Roman chariot will only go as fast as its horse(s) can run; usually this means around 30mph.
it was mostly a horse or a chariot---sometimes. A horse was used by the officers only and chariots were not used by the Roman military. (The Romans used chariots for racing). The Cavalry used horses but the ordinary soldier walked. To transport goods and equipment oxcarts were used along with pack mules.
Chariots are vehicles, they have wheels. The horse that pull them have hooves.
Roman roads were used to convey horse-drawn chariots, other small wheeled vehicles. There are many remains in the UK, British Isles.
cart behind horse
Chariots
They had horse-drawn chariots.
Chariots
Chariots.
The Horse Drawn Chariot was invented in the year 1,700 B.C.E.