Yes, these horses do exist. However, they cannot just be bred. No matter how many times you breed from the computer, or with your own horses, there is no way for you to breed one of these horses. These horses came into existance in Hong Kong. There some players took Doc 2000 v.2 horses that had stats that were all X's. They then bred them on the DOCWE Machine, and created all X DOCWE horses, and by breeding them it causes the stats to go down, and when the all X's decreased They became all double circle horses. Since then they have been sold on the internet, and on e-bay, so that they are present at nearly every location now.
These horses, start with their stats being much higher than horses you could normally breed. However they mature much faster than a regular horse. They run no differently, except they can be competative earlier. Training and feeding quickly lose their effectiveness. Usually by 5-10 races, the horse will be at the mature stage, so that the stats increase by one, or not at all. Using one of these horses is a trade off, by around 20 races you can't tell the difference between them and a regular horse. They key to a good fast horse, is depth of generations.