I’m going to put another pitch in for Camden, SC. It has a lot of the amenities of Aiken, but without the wealthy winter colony vibe. Disclaimer: I have only visited there in the winter, when riding in my part of the world was pretty limited. Camden has the Firestone-Thiel Foundation for ride out (which in every way is as nice or nicer than the Hitchcock Woods other than the in-the-middle-of-the-city setting), a vibrant horse community, access to good horse pros, pretty much everything you’re looking for.
Downsides are 1.) fire ants and 2.) hay needs to be shipped in from out of state, but both of those are true of all the horse communities south of Raleigh.
That 5 acre perfect horse property is still going to be a rare bird, but there are tons of properties in the 300 - 400K price range that meet your 3BD/2BA criteria.
I would buy one of those houses, board your horses, and wait until the perfect small horse property comes available.