No, there is nothing you can do to prevent your neighbor from filing a lawsuit against you, even if the lawsuit lacks merit.
Frank W. Chen has been licensed to practice law in California since 1988. The information presented here is general in nature and is not intended, nor should be construed, as legal advice for a particular case. This posting does not create any attorney-client relationship with the author. For specific advice about your particular situation, consult with your own attorney.
Mr. Chen is correct. A suggestion might be to investigate "mediation" - a procedure which attempts to find a win-win solution instead of a win-lose, which is litigation. Some neighbors, however, just want to fight.
The above is general legal and business analysis. It is not "legal advise" but analysis, and different lawyers may analyse this matter differently, especially if there are additional facts not reflected in the question. I am not your attorney until retained by a written retainer agreement signed by both of us. I am only licensed in California. See also avvo.com terms and conditions item 9, incorporated as if it was reprinted here.
I agree with my colleagues - there is nothing you can do to prevent someone from suing you and mediation is an excellent idea. The National Conflict Resolution Center may be able to assist: www.ncrconline.com/ If you have a homeowner's association they may be able to help too. If none of that works then a "cease and desist" letter from an attorney may help. The State Bar of California can give you a referral: www.calbar.ca.gov
The bottom line though is that you are in compliance with your zoning laws and your neighbor presumably knew or should have known the neighborhood was zoned for horses when they moved in. For reasons I prefer not to ponder some people just want to be the "nasty neighbor".
If we do not have a signed fee agreement I am not your attorney and this is not legal advice.
If you anticipate that your neighbor may try to sue you, you should start building a defense now. Consider creating a log that documents all of the actions that you describe above so that you can show that how regularly you take these actions.
Also, document the way that other people in your neighborhood address these kinds of issues. If you are doing the same kinds of things or more, it will show that your conduct is reasonable, which will be a key element to defending against a nuisance case.
Finally, think about talking to an attorney now, before a suit gets filed. You may be able to get support from other horse-owners who might face the same kind of issues, or from local stables or organizations.