I have 2 horses and board them in someone's backyard, so I'm familiar.
A 10 stall barn is pretty big, actually. A stall should be at a minimum 10' x 10' (hopefully more like 12' x 12'.
You really need to go look at it b/c barns all have different layouts and are all built differently. It's possible that it has a complete concrete floor throughout the entire barn, but that is very unlikely. Most likely (if it was built to be a nice barn), the stall floors do not have concrete in them. They are either left as dirt or packed with clay. Some people lay rubber mats down over the dirt / clay, while others do not.
A 10 stall barn on the property will significantly raise the value of the property, especially if you are looking in an area like Huntington, Central Islip, or another horsey area. In other words, you could get the same property cheaper if it didn't have a barn on it. Horse properties (even if the barn has been vacant) are more valuable.
Your taxes will change if you change the purpose of the structure. In other words, if you add a bathroom or hot water or something like that, it can and will change your taxes. You need to look into that before undertaking any major renovations. Also, barns are NOT structures like houses. They are not built / wired for heat, major electricity like AC and entertainment centers. Barns should be designed to be open and airy (as fresh air and good circulation are a must for stabled horses), so the barn is not going to be insulated like a house. This makes it very expensive to heat (or you have to completely renovate the building to insulate the walls.
Unless the wiring is brand new, you will absolutely have to redo all the electric wiring. Barn electricity is usually just for lights and small things (electric clippers, e.g.) only and cannot handle an overload of electricity.
The good news is that GENERALLY barns are just a big open building and the stall walls are put in after the outside structure is up. This makes it easy to remove the stall walls. However, it's possible you'll have to redo the floor b/c it likely won't be solid concrete. The stalls are likely dirt with a concrete aisle / concrete in the aisleways. However, also remember that if it's a center aisle barn, it likely has sliding doors on either end that are in total at least 10 feet wide.
If it's a shedrow style barn, it's really not useful for anything else except horse stalls and storage. Shedrow barns have no center aisle - so basically the horses go staight into their personal stall from the outside - there is no 'inside' to the structure, just freestanding stalls usually.
It really depends on the barn and the layout. Be prepared to deal with tax increases, etc. Also if it's a very horsey area, be prepared to deal with horse people as neighbors - That means there will be manure storage on their property. All towns have strict rules and most people put it in an dumpster and have it hauled away... but you may have horses as neighbors. If you're not an animal lover, you may not appreciate it. (I'd personally love to have my horses in my backyard). Also you need to check the zoning regulations. MOST of these horse towns have tough town boards that you may have to go to gain approval (Central Islip, e.g.) to change existing structures. They are protective of their horse properties and may not want to give you the permit to change the structure. There will also, like I said, be tax consequences.
If you have any more questions, feel free to FM me. I've been involved with horses for years (was a professional rider and have managed several barns along the east coast). I'm a little familiar with barns.
ETA - To be clear, you are looking at RAISING your taxes if you convert the barn into a place with a loft, etc., especially if you add a bathroom. This is also not something you can hide from the town, as there are serious consequences for getting caught. Also, it is not necessarily true that the barn has a hay loft. It may not be possible to convert the barn into a huge room with a loft for sleeping. Even if there is a hay loft, there wouldn't be access to it from inside the barn. The loft would likely be accessed from an external staircase or in many cases, just a ladder.
You really have to look at the barn to know what you are getting into. You are most likely looking at completely rewiring and renovating the entire thing. It will be very expensive.
Also, if you are looking in a very horsey area (e.g., Central Islip on Connetquot Park), many of the horsey neighbors will be unhappy to lose another horse property (though it's yours so you can do what you want with it). However, your home will have more value with a barn in the backyard than with an entertainment area / loft, especially if it's in a horse-friendly area. (Lower taxes with the barn and higher value for the land)