I live on horse property in a sort-of horsey neighborhood. The parcels are small...only about 2 acres...and some homes have septic easements on the neighbor's property (meaning the drainfield is on the neighbor's property). In that instance you can't have livestock on a septic drainfield.
But if this is just a matter of your neighbor not wanting your new tenants to have really big pets, um, NO. She can like it or lump it.
Now...just be aware that your neighbor may do really dumb or nasty things that could make your tenant's life miserable and/or make life difficult for you. All it takes is a few handfuls of buttercups over the fence to render your pasture useless in a season. Or she could complain to the health department or land use department about manure management issues or flies or whatever.
If you can, I'd try to find out specifically what the neighbor objects to about the horses and mitigate those concerns if it is not expensive. Is it the manure stink in the summer? Is it flies? Is it them eating four feet of her garden through the fence? Could they chew on her shed or other outbuilding?
To mitigate you could make sure to have a proper manure compost system. Require your tenants to keep manure scooped. Is the property large enough to put a six foot buffer zone between where the horse access ends and the property line is - such as an extra wire horse fence inside your property line?
I dunno...just some thoughts. Your neighbor sounds like a PIA. Good luck!
P.S. I love my neighbor's horse. He greets me every day when I come home and his property ends only about 15 feet from my dining room window and deck. Yes, I do sometimes smell manure in the summer but for us animal people that's no problem. And he DOES eat quite a bit on MY property...those necks are loooooong. But he's way nicer than most people and he makes the best noises ever! :-)
You never need her permission to do anything. Tell her to stuff it.
Ann is correct. You must be legal and you must be fenced and then it is not her business.
Check your local zoning and land use regulations.
You own the property, unless it is zoned where horses or livestock are not permitted, she has no say in it
Of course not.
I currently rent a house out that has horse privileges. I am not renewing lease with current renter, and have been informed by my neighbor (who is friends with current renter) that I must get her permission when I choose the next renter, and she won't stand for any horses. I have a renter ready to move in with 2 horses once they leave. Do I need her permission?