Knowledge is definitely power. To properly love, respect and care for the animals we come into contact with, we definitely have got to understand their species.
As a horse owner myself, I feel for those horses who are tied up. Do they get any run time at all? That's what horses do ... they run and LOVE to do so! Read, read, read as much as you can about the animals that you are attending to and you will be a great example to the rest of the folks you are working with, on how to attend to each animals' needs. In addition, you will be able to better answer your own question about what you can/should do to improve the barn conditions.
I am clueless about pigs so I am sorry to say I can't help out in that area. My hubby is more horse savvy than I and spends his time researching them. Me, I am a bun-slave to the nth degree, I have one who is treated like a queen and will be adopting/rescuing more. So when I saw that rabbits are a part of the barn animals, I immediately wanted to ask ... what happens to the bunnies when they are no longer babies?
Talk to you soon and good luck with this situation.