I'm living in a small town. Here are the reasons why I hate small towns. There are no high paying jobs and can be a long commute to the city where the high paying jobs are at. Also there is nothing to do in town. You can't have a horse in a city.
Most Helpful Guy
There are stables to keep horses all over the place. They are not in any way restricted to small towns. You might not find them in the inner city, but there are plenty in the suburbs and surrounding areas.
If you want horses on your own property, anyplace where you can buy (and afford) a property large enough to keep horses should be OK. Again, most suburbs should be OK for this, except for maybe a few very restrictive places.
Keep in mind that they require a lot of your time. If you stable them someplace you will need to go there regularly.1