"What are some (aesthetic) "deal breakers" on an otherwise breeding quality horse for some of the other posters? Or even pedigree problems that would cause you to not breed a phenotypically superior horse? Are there any?"
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Again, I think "aesthetic" is relative. What one may think is for a horse aesthetically pleasing, another may not. Someone may like a more reachier, scopier type of horse, and another may want a shorter coupled stouter type of horse. I think aethestics are driven by what someone does with their horses. Sure everybody would like a pretty head and a nice color, but neither of those are a make or break deal to me. I am personally most driven by "What can he do".

As far as pedigree problems for me personally, there are certain horses or "families" I just dont care for. So I tend to stay away from them. Irrigardless of what they look like or have done.
I also when picking a stallion, not only does he have to have physically what I am looking for for that particular mare, but he hails from a sire who is by a sire of sire's, and his Dam is successful herself, and has produced successful. If you really look, most all great sire's come from incredable dam's. Usually, if she is so so, as a sire he will be so so. If she's a nobody and didnt produce anything else of note besides him, his chances of being much of a sire is not great to say the least. That is my experience anyway's. I will forgive a sire line, much more then I will forgive the maternal line.