It kind of looks like a wrens nest. If its small and sort of like a pouch with a small hole, thats what it is. Wrens like to nest fairly low, so I'm betting thats what it is. If there are no eggs in it I wouldn't worry to much about letting the horses in the area. Birds in general and wrens in particular build nests very quickly. They will build another if they don't like the horses nosing around.
I have had wrens build nest in the pockets of jeans hanging on the line to dry, thats how fast they are.
"Until one has loved an animal, part of one's soul remains unawakened..."
- Anatole France