Never had as many as you asked about and I think our highest horse count was 26 or 27 counting all of them (mares, foals, stallions, yearling, our geldings we kept to ride).
Minis-I only had 1 mare and her and the stallion stayed together all the time. Had a small pen attached to one of the stalls and the mare would be confined to it when foaling time came. After a few days when the foal had figured out how it's legs worked, they were turned back in with the stallion. Foal counted on mom for food but dad was the babysitter/playmate.
Dad with 2 of his kids following him (mom was probably hiding in the barn).
Our paint stallion was kept in his own corral with access to his little section of the barn. A gate with a strand of smooth wire across the top is the only thing that separated him from the other horses, including mares. It wasn't electrified but since the fencing around the pastures/corrals was electrified high tensile he thought it was or at least didn't care enough to test it. Pastures came right up to his corral. Only time we had an accidental breeding was when hubby forgot to shut his gate, which happened more than once but only one OOPS. He ended up being a pretty good oops though. This is him and his mom with dad just on the other side of them. 009_9.jpg
Only ever did live cover and his first year we bred him in hand. After that He'd be in one corral and I'd take the mare (my mares) to be bred and put her in the adjoining one. Open the gate, let them do their business then I'd put him back in his corral and take the mare back to her pasture.
Made the mistake of having 6 mares due in about 6 weeks of each other and by the time it was all said and done I think I spent about 2 months staying at the barn every night. I was a walking zombie by the time I got to move back to my own bed every night.LOL
Pasture scene that shows some of the mares and foals that crazy year. 023_02A.jpg
We had no outside help, you just do what needs to be done. Most often I sold what I wanted to sell by the time they were 2 so I only had the basic training in them. Once the market went caput I had both stallions gelded. Down to 12 horses now and that's pretty manageable since we have plenty of pasture.