No, they were not bred like animals. Perhaps there were isolated individuals who attempted it, but it was neither widespread nor common, nor (apparently) ever recorded by someone who actually did it. That alone is compelling evidence: those who are serious about breeding domesticated animals (cattle, cats, horses, et al) are usually not only serious, they are damn serious. They document bloodlines and genealogy, thoroughly examine and document offspring, plan future matings, etc. There are purebred horse lineages well documented back a few hundred years or more, including through antebellum South. If someone thought what they were doing with their horses could have been applied to their slaves, they would have kept records. So, if what the OP described really was common practice, we would have records.
Let’s look at some math…
A horse is ready to breed in what, 3-4 years? Not just that it’s sexually mature, you need time to know if you actually want to breed that particular one.
“Average” human generations are roughly 20 years. While a 15-year-old boy might be sexually mature, he probably hasn’t finished growing yet. How would a slave owner know who was going to be the biggest of the boys (and thus desirable to breed)? Wait until they were full grown, easily 18-20 years.
So after 20 years of breeding you could achieve maybe 5-6 generations of horses, and exactly 1 generation of human. Let’s assume someone actually did this, for their entire adult life of 60 years (abnormally long for that time period). They would be able to breed 15+ generations of horses, but only 3 generations of humans. Three generations is hardly enough to identify desirable and “reproducible” traits.
After saying all that, I must share my palatable distaste for comparing human reproduction to the breeding of livestock. I only did so because it was raised in the OP: “…would breed slaves … just as any other breeder of animals would.” Whatever other atrocities were going on (yes, there were plenty, and no, I’m not defending any of them), no, they didn’t “breed” slaves like animals.