I’ve moved multiple states onto horse property twice, and both times I saw the property that we eventually purchased on realtor.com before even finding a realtor. You can dial in your search for distance from a specific point, then acreage, and include keywords (barn, stable, horse, etc.)
Zillow is another engine to use, and has the benefit of houses that might not be on the market (owners can set a “make me move” price.)
Towns often have their own GIS page with property info and satellite imagery, which can be really useful.
If there’s a state/city/region horsey FB group, that can be one more avenue to explore, and you might find property not yet on the market or listed as FSBO with a “in search of” post.
A realtor who is horse literate is vital, once you’re really ready to pull the trigger and move. It’s amazing how much property is marketed as “horse friendly” where HAAAAHAHAHAHA no, wow, it’s really not. You don’t need to go see everything yourself, your realtor can do quite a lot of that legwork and take properties that absolutely won’t work for you off the list.
Good luck!