If you are looking in a somewhat horsey area find a real-estate agent that specializes in horse farms. They can usually have an extensive personal back ground with horses. Grew up on a farm, worked with and or owned horses for years and know the drill.
There should know where the “holes” are with a horse property.
They should be well versed with the local horse zoning laws, ordinances.
If a property is zoned for horse activities the existing zoning can’t be “downgraded”. In other words if they property is zoned for 5 horses it can’t be change to 4. The existing zoning can/will be grandfathered. But it can be modified with other restrictions. Which may effect it value to future horse property buyers.
As other have said check the availability of service providers. Vets, farriers, feed, hay and bedding suppliers. If it is sparsely horse populated and or the property is on the outskirts the travel time may make if difficult to get reliable Vets and farriers. Or you will have to pay a larger farm call fee. Farriers may be booked up.
A good horse farm real-estate agent should know about these things. And provide numbers to call and check on availability before you purchase. Having more than one horse makes taking on a new client more attractive.
Having a Home Depot, Lowes etc and or a good Hardware Farm services business close by is extremely handy.