1 side says, you're being too nit-picky...but that really only comes down to the recylcing part
The other side is:
I'm paying board, so there is no reason for this place to be a mess and garbage to be over flowing!
I'm sure that the "i'm paying for this" is also why some people feel entitled to NOT clean up after themselves. No clue where you are from, what the background is, ect... but I figured out very quickly when I went to college that you can lump people into 2 general groups. Those that had things done for them, and those that had to do things for themselves to get anything.
Sounds like a lot of the others that board at your barn are the ones that are entitled to what they want, and they havn't had to do a whole heck of a lot for themselves, they said "mommy I want _______" and they got it.
But all in all....if you want that stuff to go to recycling, you're the only one that can/will make that happen, you can always try putting a recycling container beside the garbage can. Inform the barn owner that the garbage is overlowing, and sweep up after YOUR horse and let the others go. Can be hard to do when you like things to be neat & tidy but eventually the barn owner or other horse owners will notice