There are no horse breeds in Sim 3 Pets.
What? but ... but ... but ...
In CAS we're shown a tab labelled "Breed" and are offered a number of choices. Alas, these so-called breeds are only there to help us imprint limited colors and conformation on the animal we're creating/modifying. In game, if we select a horse, no where does it show us the breed of the animal.
In Adopt a Pet, we are sometimes given a choice of breeds among the Mixed selections. These appear only to give us some notion of how the pet will appear.
Were breeds actually an integral part of the game we'd be restricted as to horse colors in CAS; for instance, no Arabian could exhibit buckskin or Palomino coloring, nor would it have spots or feathered fetlocks.
In Sims 3 Pets, horse breed is a matter of personal imagination and roleplay; otherwise, the term is meaningless.
Some clarification about Wild Horses and Mustangs. First, the only truly wild horse is the Przewalski's Horse, which is native to Mongolia. Otherwise, all free-roaming horses, including Mustangs, are ferel horses; meaning, somewhere in the past their ancestors were of domesticated stock. While there is some indication that equine species existed in North America in early history, all of these died out between 10,000-12,000 B.C. The Mustangs we're familiar with today were introduced by Spanish conquistadores and were principally of Andalusion, Arabian, and Iberian lineage.
In Sims 3 Pets, any free-roaming horse not owned by an NPC or other Sim is a Wild Horse. There are a couple of instances where the game uses the terms 'Wild Horse' and 'Mustang' interchangeably. While this may be confusing to some, the reference is largely irrelevant because, as I said earlier, breed is absolutely meaningless in the context of game play. Shakespeare might have put it this way: a horse by any other color (or conformation) is still a horse.
Now, it happens that my Sims raise Arabian horses, but this is only roleplay on my part. My foundation animals (the original horses I made in CAS) were done up to closely resemble the real-life Arabian Horse standard, but it's only roleplaying; insofar as the game is concerned they're still just horses. Were there a real Arabian breed in game, horses would be born with the following traits: intelligent and spirited. They would also have the Lifetime Reward of 'Desert Pony' built in, but this is not the case because breed in Sims 3 Pets is irrelevant for anything except limited coloring and conformation in CAS.
Finally, the game makes no distinction amongst horses per their value. In real life purebred animals, like Clydesdales, Thoroughbreds, Quarter Horses, and Arabians, sell for much more than "mixed" breed animals. Likewise, their stud fees are infinitely higher; yet, in Sims 3 Pets the value of all horses is egalitarian. Traits, training, competitive standing, and parentage are the only criteria affecting value of horses. Breed and purity of bloodline are irrelevant because they are not a component of game mechanics.