Check your state statutes. If you were not notified of restrictions or covenants at the time of sale, and if they were not a recorded public record, including being a part of the plat for the development, there is a really good chance that they are not legal/valid/enforceable. At the very least you have cause for action against the seller who failed to disclose covenants. The county should have been able to find covenants/restrictions when you first requested, and since they did not, I'm wondering how they are showing up now, six years later. Check the dates they were recorded, and compare with the date you closed on your property. If it was after your purchase, they cannot apply restrictions to your property--it is no longer theirs to do so. If it was not WELL before your purchase commenced, you have cause against your seller.
Typically normal nuisance laws can and do deal with odor, pests, noise, health, etc., which is their legitimate concern.
You also need to read the whole set of covenants and see how they can be changed; you also need to become conversant with any state statutes that deal with this. More and more states are passing laws to protect those who live in associations with restrictive covenants--making sure that the covenants are not heavily biased against homeowners, and that they have collective control of the association. As an earlier poster mentioned, votes by a large percent (typically 60-75%) of the votes can usually change the covenants. Unless there are significant differences in some properties, it is usually one vote per property. Since you own several, that would mean that you have several votes say in making a change.
If you do decide to try to make changes, make sure the real nuisances are what are addressed, not the cause of the nuisance. Chances are pretty good that with better care the property owner being sued could have better kept his livestock so that they did not become a nuisance. You might also check into the zoning uses for your development. Zoning typically allows fewer uses on smaller properties than on larger ones. Chances are fairly good that that property owner has more livestock on his land than zoning allows.