Just my opinion after wrapping up a similar search. The horsey piece is my dream, and my husband is supportive, but it was not his top priority.
We both agreed that, living in New England, we wanted an old, historic home, so that took priority. It quickly became apparent that places advertised as "horse properties" in our price range were typically new construction, trailers, or somewhat dated mid-century construction. Our realtor told us that, in our area and in her experience, horse folks either put all their money into their barn and fencing, or they put money in their house. But they didn't put money in both. I would say that was born out in our search. We saw some gorgeous barns all up-and-ready, but the houses tended to be a mess and had lost all the historical features we were looking for. We also saw plenty of houses loaded with character, but with barns that were not ready for anything to live there.
In the end, we went for house first, buying a sweet 1790's cape that was impeccably cared for. Wouldn't you know, it is the only house we looked at that didn't even have a falling down barn to work with. There are 5.5 acres out back, so we will be starting from scratch on the barn & fencing in the next 1-1.5 years after the dust settles.
I don't write all that to say that the way we did it is the best- just that, in our experience in New Hampshire, getting the house we wanted with the barn and fencing we wanted wasn't really an option, so we had to initially choose one over the other (unless you approached 7 figures, which we were not in a position to do. I won't assume you aren't, so if you are, you probably have a much better chance to get what you want in both a house and a barn).
Through the barn where I ride, I've connected with someone's husband who owns a fence and landscaping company (with plenty of horse experience), and he was out here today to start clearing the debris from what will be the first pasture. I agree with the extension recommendation above- I am going to be talking to them next week for advice on how to start seeding the cleared area with a long-term goal of having usable pasture. The drainage issue will be the next conversation.
Good luck, and above all, have fun! Having recently moved from the Midwest (Michigan), my sense is that it's still a buyer's market there, so if you don't have immediate time pressure, my #1 piece of advice would be to be really honest with yourself about your priorities in both house and land, and look around to try to find what ticks most of the boxes. If you don't have to decide quickly, it's great to shop around some.