I don't know the laws in Ohio, but in Oklahoma, you would have to explain to the Humane Society why your horses were thin when you see them so often. Even though you are paying the BO to care for your horses, they are ultimately your responsiblity, so you will bear some of the responsibility. If the Humane Society decided a seizure is warranted, and your horses are seized as well, you are looking at a potentially lengthy court process to get them back.
That being said, actual seizures are pretty rare. Animals are only seized under "exigent circumstances." Meaning they are only taken if it is a dire emergency. If the horses are just thin, the BO will likely just be given a warning to improve the care that the animals are receiving. How the BO will react to that is anybody's guess. Once you are on their watch list, you tend to stay there and they can show up at any time. You may also be given a warning, as would the other animal owners at the barn.
We rescued some really skinny horses last spring. They hadn't had time to put any weight on, but someone reported us. Sheriff's department handles the investigations and they came out. We showed how we had just got the horses, showed him the feed (he also showed up at feeding time, so he could vouch that the feed in the barrels was not just there for show).
He showed up on his own every couple of months after that, or whenever someone reported our horses...again. They were all gaining weight nicely except for the daughter's mare, and she was under a vet's care. Vet could not figure out what was wrong with her. Mare would get better and start gaining weight, then drop the weight off and get skinny again. Deputy said she was skinny, but not emaciated - but the mare eventually died. Guess that's the hazard with rescues.
Plain Old Dee, horses Dancer and Rain I believe in dragons, unicorns, good men and other mythical creatures!