I'm going to jump in here also with an example of how yuo can't go by bloodlines to know the breeding quality of any horse without trial and error.
When I first started in the minis, some 28 years ago, I didn't have the money to go buy a horse. My first horse was given to me because his back feet were deformed, but, it wasn't his fault. It was human err. His owners lived in Houston and the ranch was here in Austin, TX. They came to the farm once a year but had a hired hand that took care of the horses and the cattle. Obviously, the hired hand didn't take care of the horses in this case. Mud had built up into his back feet (good old Texas black gumbo clay) and they rolled to the outside. When they returned the next year, they found the colt crippled, the damage done. Into the picture I came. They gave me the yearling colt and his two year old sister. These horses turned out to be 3rd. genertion American Miniature horses. NC and his sister were from a Freeman horse named Freeman's Mini Red Star. The Freeman line changed to the Ayers' line. If you know the older lines, most know of Ayer's Mini Red Man. I never have found out if Red Star was a son of Red man's or a "litter" mate, lol, but, my stallion looks identical to Ayers Mini Red Man Jr. I've never heard much of the Dams side, Clarehearsts Misty Mindy, but she was also first generation miniatures. She was Komoko top and bottom.
When these two horses died in their late twenties, they had never produced a dwarf and Misty had a foal just about every year of her life after she turned two. I still have NC and to date, he's never produced a dwarf. He's somewhere around 22 years old now.
Now, my horses coming from the Freeman/Ayers, Komoko lines, are known under the name of Skyline. After I aquired my stallion, I started going to horse sales and buying unknown small ponies for pennies on the dollar. I knew what I was looking for. Out of those horses and some very good friends letting me breed to some of their very good stallions, I started producing Champion winning halter horses out of unknown lines.
Bottom line, the pedigree has but a little of the equaision on breeding good horses. Conformation, and knowing how to read horses by the shape of their heads for good temperment is the biggest part of good breeding.
Pedigree helps because you get some history with the horse so you can get an idea of what's behind the horse but it isn't as important and labeling a "Bloodline" as a bad bloodline. I love the Bond line and I love the Dell Tera line. They usually have beautiful eyes and heads. Were those horses really Bond and Dell Tera bred horses? Who knows. I have a couple of stallions that have Bond Tiny Tim in their background. Is he close? No. He's well back in the genes, but, I know he's there. Does it stop me from breeding that stallion? Not a chance.
In the years I've been in minis, I have yet to produce a dwarf, not even a minimal. I've been very lucky. Is that a brag? No, it is not. I look for any "sign" of a mare carrying a possible dwarf gene. Do I breed that mare, no. I will sell her, if I was negligent in buying her in the first place, with the understanding to the new owner that she may be a dwarf producing mare and I do not reccomend her being bred.
Like others have said, read, look at photos, ask questions, learn and try to teach yourself to look for the suttle look of a possible dwarf carrying horse.
A friend of mine bought a mare, unregistered, at a mini horse sale and I didn't see the mare up close before she bought her. When I saw the mare in the trailer, I noticed the mare had a lower lip that didn't look right. Teeth were fine, just the lower lip was a little bigger than it shoud have been. She was bred to a really nice tiny black stallion that went thorugh the sale also. Low and behold, the mare kicked out a dwarf. Just that lower lip gave her away. Other than that, she's a really nice mare.
I'm telling these long winded stories just do people can see. Don't judge a bloodline, learn what to look for and ask questions. You may not always be told the truth, but, at least you tried.
Good luck to all in next year's foal crop.