A horse stable is not a "noxious and nuisance businesses" and there is no reason for you to be "afraid for [y]our privacy, security and quality of life".
But be that as it may, if an owner's property is within the HOA, then the owner has to abide by its rules. It is not clear if the property at issue is in the HOA or not - if it is not, then you have no standing, outside of the area's zoning ordinances, to complain. If the area's zoning allows for horse stables, then the owner is well within his rights to open and operate a horse stable. If his property is within the HOA, he must abide by its rules. A local attorney should be able to review the HOA and advise you. The State Bar of Texas can give you a referral: www.texasbar.com
If we do not have a signed fee agreement I am not your attorney and this is not legal advice.