I think that might be hard to do. I see lots of ads here where people asking to trade off working in a barn for $ off the board for their horse. Might be same in your area. Doesn't hurt to go and ask though. I would wear slacks, top with a jacket with proper footwear. No jeans or flip flop type of things.
Find out who the owner or barn manager is and call them to see when it would be convenient to stop in and talk to them. Shows them you're considerate and viewing the work as an actual job, not just something for fun. Be honest about your abilities also.

What's slacks?

I agree with Karla. But to just be honest and don't take it like a joke. One of my family members is in the same suitation but about a different type of work. She has noticed that the people dressed proper and were well-mannered usually got the job. I hope that helped a little.

slacks are dress pants.

Best thing to do is call around. Ask if they are looking for help. If they say yes, set up a time and be on time!

Go dressed to work. But make sure your look is clean and well put together. Breeding farms and boarding barns are a business.

If they like you, they may ask you to demonstrate your skills. Always be polite. Don't talk bad about other barns.

i would just try volunteering, more barns would rather have volunteers than have to pay workers