Pony girl, first a matter of semantics. When you are writing about a paint horse or a pinto horse, you are writing about a color. When you are writing about a breed, the breed name is always capitalized: e.g., Paint, Pinto, Quarter Horse, Thoroughbred.
Yes, it is nit-picky, but it's one of the things that enables horsemen to know they are dealing with someone who is knowledgeable.
Thing one: the American Quarter Horse Association, which is the breed registry and makes the rules for what can-- and can't-- be registered as a Quarter Horse, frowns deeply on the registration of any horse with excessive white markings. Prior to 2004, excessive white markings, including paint or pinto markings (note that "paint" and "pinto" are not capitalized, e.g., we're talking color, not breed) were cause for refusal to register a horse.
This is the current rule governing white markings in Quarter Horses: Rule 205 (d):
"(d) White Markings: A horse having white markings with underlying light skin beyond any one of the following described lines shall be eligible for registration by AQHA only if it is parentage verified through DNA typing the offspring, its sire and its dam. Breeders should be aware that the American Quarter Horse, while long recognized, identified and promoted as a solid-colored horse, can and does occasionally produce offspring with overo paint characteristics. Such markings are uncharacteristic of the breed and are considered to be undesirable traits.
"The following notification shall be placed on registration certificates of horses exceeding these marking limitations:
""This horse has white markings designated under AQHA rules as an undesirable trait and uncharacteristic of the breed."
What this means is that you may register a Quarter Horse that has excessive white markings, including paint and pinto markings, but you sure as heck are not going to have much joy showing such a horse against Quarter Horses that don't have excessive white markings. For this reason, you aren't likely to see Quarter Horses with such markings in the mainstream Quarter Horse events. Breeders will continue to do what they did prior to 2004, which is register the horses as either Paint or Pinto, only now they will be "double-registered" as Paint or Pinto, as well as Quarter Horse.
With regard to Thoroughbred horses with paint or pinto markings, there are a bunch:
http://www.thepaintedthoroughbred.com/
http://onetrickponyranch.com/JC%20TB%20FILLY.php#
http://www.painteddesert.net/apache.html
http://www.whitehorseproductions.com/ecg_basics3.html#pinto
The Jockey Club, which is the organization that registers Thoroughbreds, has never cared a whack what color the horses are as long as both the sire and the dam were registered in The Jockey Club stud book or one of its overseas analogues, like the British or Irish or French stud book. There are white (not grey) Thoroughbreds, palomino Thoroughbreds, buckskin Thoroughbreds and horses with every kind of marking you can imagine.