http://www.equineboard.com/minature-...-pony-108.html
I already made a posting about the difference between a horse, miniature horse and pony after we had some rather confusing posts about such things.
As to how minis came about, they were probably selectively bred from abnormally small horses. Some minis are stockier like ponies but they are more like mini drafts than shetlands, based on the relative structure and proportions.