There are strict regulations on discharging water from a waste system above ground. There would or let's say should be no bacterial contamination. The water depending on the system goes through multiple stages and is sterilized before use in an irrigation system.
...if the aerobic system is working perfectly, yes, it's reasonably clean, but using the word "sterilized" isn't exactly the case. A system without chlorine addition, well functioning, there is still a high level of fecal coliform in the above ground discharge - 10,000 CFU/ML is what is considered "clean" discharge for an aerobic system.
For a system that uses a chlorine system as the last stop before the sprinkler heads, 200 CFU/ML is still the maximum, although it might be lower...but "sterile" is highly unlikely.
For reference, zero is the standard for drinking water, and they typically close public beaches to swimming at around 250 CFU/ML.
Draw your own conclusions, but I wouldn't want horses on a sprinkler based septic system.
Again, in the north we have systems with dramatically larger and deeper leachate beds as sprinkling is simply not an option when things turn to ice and snow...so if you have a good system properly installed and deep enough a horse is unlikely to damage anything.