What breed of horse was used to pull chariots in the years of the Roman empire?

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.