Ponies are a different category of breeds to horses.
If you imagine that dogs are in broadly two categories, chihuahuas(sp?), terriers, toy breeds, handbag sized dogs, pugs, etc are the dog version of ponies.
Labradors, German shepherds, Newfoundlands, pointers, greyhounds, Huskies etc are the dog version of horses.
A cross breed or mongrel that is small is still a pony - large is still a horse.
Most of our native to the UK breeds are ponies. They tend to be intelligent and resilient, having been historically bred to carry a small farmer all day and maybe a sheep or deer carcass, or pull coal carriages up and down mining pits all day.
Our horse breed natives include the Suffolk punch, a huge boned slower animal, who needed huge strength to pull heavy wagons on the farm all day, and able to be "parked" quietly for long periods of time, but quick wit, ability to think and be clever about where to put his feet weren't required and the accompanying personality tendencies to shying, making things up to do when bored and generally being trouble certainly went desired. Similar story to the black horse of England now known as shire horses, and clydesdales. Racehorses were lighter horses, who had one job, to go fast.