We bought our small acreage a year ago, here's what we focused on:
1. WELL- this was a huge point for us, definitely pay the extra money to have a well expert come out and do the flow per hour test, particularly if you need to supply your barn from the same well as your house. We will be building a barn in the future, and will need a new well to keep the barn going without a negative hit on our house.
2. BUG/PEST PROBLEMS in all structures. I don't think anyone mentioned this, and maybe not as big a deal for you since it's a newer property (our house was built in 1790)- be sure you have a thorough inspection for termites, powder post beetles, etc. that could be compromising the integrity of the buildings.
3. In my state, there are tax incentives for farm properties if they are kept in "current use" - i.e., it is currently a horse property, and if you keep using it as a horse property, you keep that low tax rate, but if you ever remove horses, the tax incentive goes away. Be sure your realtor is smart and on top of this, or ask a tax professional if you have any questions. Don't want any nasty surprises in the future.
Otherwise, I would advise finding the best inspector you can who will be honest and tell you every painful detail about the roof, electrical, plumbing, etc. in all structures on the property. Even if the inspector identifies things you don't plan to fix right away, you might be surprised how much a motivated seller is willing to fix- or give you the cash directly to handle the hassle of fixing on your own. I agree with whoever said the electric in the barn looks dicey in the pictures (I am not an electrician...), and having an inspector's report on that sort of issue can be really helpful if you get to the point of making an offer.