I have quite a bit of experience in role playing (more experience than I'd feel comfortable admitting to lol), and the group I role played with had a thing about historical accuracy. We played several games set in particular periods of history, so it helped to know a lot about how life worked in those eras. So I could potentially answer quite a few of your questions.
Assuming that this is a medieval era that we're talking about, where horses were more of a necessity than they are now, it would depend on the person. In those days a horse was another mouth to feed, and you didn't keep any more horses than you could use unless you were wealthy or breeding them was your profession. A farmer would likely only have one or two multi-purpose horses: he could only use one himself, and one for his children when they were old enough to work the land. Nobles would likely have at least 4 to use with carriages for transportation purposes, possibly even more if they owned farm land. Young noble males often had a riding horse of their own, as well.
If we're talking about adventurers of lore and legend, they'd only have one. Even as late as the old west, a horse was much more than a vehicle to people in that kind of profession: it was a beloved companion who could save your life. You needed a horse you could trust and one that trusted you enough to do things that were against it's natural survival instincts (riding into battle instead of away from it, galloping down a sheer cliff face, to keep running when it's exhausted, etc), and it's difficult to develop that kind of trust with a full stable of horses. Remember that scene in the Lord of the Rings: The Two Towers, where Aragorn went over the cliff and his horse came and rescued him? That's not fiction...horses were actually trained to do that kind of thing at one time.
If the building in question is like an inn, where travelers would seek lodging, horse accommodations would be sparse if they existed at all. Housing a horse was an extra expense that few could afford, and those who could would be more likely to seek out a professional stable to care for their horse while they didn't need it. A stable would do all the necessary comfort maintenance (hoof cleaning, shoe maintenance, de-burring), while an inn likely wouldn't (not that you'd likely want them to anyways...it would be like getting the guy at the car wash to overhaul your car's engine lol). So an inn would house maybe two horses at the most...four if you're lucky.
Exercise yards are a relatively recent development. In medieval times, a horse breeder would have one for training horses to be ridden, a noble would have one for teaching the family how to ride them, but anyone else wouldn't have a need for it. Since a horse was part of your everyday life, it's a sure bet it would get all the exercise it needed...and possibly then some. Land was (and still is) expensive, and areas devoted to horse exercise would be better utilized by planting more crops or building a functional structure.
These are just generalities based on assumptions. If I knew more about the type of person this "dorm" was meant to house and the era it takes place in, I could potentially give a more accurate answer.
