In my humble opinion, Big South Fork is the absolutely best single park to ride in the southeast!  It's about a 3 hour drive for me to get there, and I'll try go 6 or 7 times a year.  I never get tired of it.  The trails vary from flat to gently rolling (if you say up on the plateau) to steeper and rocky (if you ride down into the gorge). 

The Big South Fork does a good job of keeping the trails maintained both through the use of paid park maintenance personnel as well as a good number of volunteers to work on the trails.   There are 180 +/- miles of horse trails in the Park, most of which are designated horse trails (horses and hikers only) but some being multi use (bicycle, wagon/carriage, horse and hike).  They are really trying to minimize ATV and off road vehicle usage in the Park, so you don't really have alot of encounters with those types of vehicles except on a few designated ORV trails (which are really more like dirt roads, not alot of fun to ride horseback anyway).  There are many rock formations, caves and overlooks in the Park.

Places to stay - (1) Bandy Creek Stables is located in the "heart" of the southern portion of the Park.  The stables are operated by concessionaires (Gretta and Bobby Gene York) but the property is owned by (and located inside of) the park itself.  The campground is owned and operated by the National Park Service and is located about 1/4 mile from the stables (unfortunately you can't camp with your horse).  The stalls are supurb, I never worry about my horse being left in one of the stalls even thought I'm a little ways away.  They also offer outside pens (4 corral panels arranged in a box, not covered) which I prefer to avoid if at all possible.  They do have a couple of pens for rent which would accomodate a couple of horses each.  Those are also not covered, so they get muddy if they've had very much rain.  The advantage to staying here is you have direct access to many trails in the southern portion without the need to trailer your horse.  (2) True West Campground & Stables is located on the western edge of the park.  This is on private land with a 1 mile horse trail to access the Park (you have to ride that same mile in and out every day just to get to the Park).  They offer covered stalls and maybe a pen or two.  The stalls are adequate, but not quite as nice as those at Bandy Creek.  (3)  Saddle Valley Campground and Stables is also located on the western edge of the park (just down the road from True West).  This is also on private land with a 1+ mile horse trail to access the Park (again, ride the same trail in and out every time).  They also offer stalls but have some nice roomy paddocks and small pastures. Probably the best choice for horse pens, but not the best for trail access.  (4) Timber Ridge Campground Stables is located on the very western-most edge of the park directly adjoining the Park.  Stalls are adequate, but I don't know if they have any pens.  You can access a couple of trails directly from camp, but most of the trails are located far enough away that you'd want to trailer your horses out.  (5)  Honey Creek Horse Camp and Zenith Horse Camps - both are private campgrounds/stables located on the southern edge of the park.  Used to be there was not much riding available in the area, but the Park has been developing more trails down there.  They are probably the 2 most remote campgrounds in the park.  (6) Station Camp Horse Camp and Bear Creek Horse Camp are designated horse camps located on the eastern edge of BSF (Station Camp to the south and Bear Creek to the north).  Both are located inside Park boundaries and operated by concessionaires.  These horse camps offer pipe stalls and/or high lines at the back of each site (no stalls or pens) -- not the best idea if you're planning on leaving the horses unattended for hours.  There are quite a few private cabins with stalls for rent in the area, but all are located on private land.  For my money, I would stay at Bandy Creek (the stalls get reserved fast, so call early during peak seasons).

East Fork is a privately owned facility located 20 or so miles west of Big South Fork.  They do offer decent stalls and campground.  They do charge a fee to day-ride if you're not camping with them.  I have ridden those trails once and have never been back.  I just can't justify paying to ride trails when I can travel another 30 minutes and ride nicer trails for free!

If you do plan to come to Big South Fork, invest in a Trails Illustrated map (put out by National Geographic).  Big South Fork does a good job of signage on the trails.  Combined with the TI map, you really don't need a guide to find your way around. 

We were at Zenith in 2008 and there was a barn with decent stalls.  However it is not very close to the sites.  Within walking distance but not where you could see your horses while sitting around the campfire.

We enjoyed Zenith.  The bath house was nice and there was a multi-purpous room for the campers that had a full kitchen and dining area and TV.  We made use of this quite a bit because it poured down rain for 2 of the 4 days we were there.

Wow Sommerset.  That is great information!  Wish I had seen it sooner but alas we are packing up to leave for home in the morning.  Never did get to ride at Bandy Creek.  Would have loved to do the trip you described.  We ended up taking a day trip to Lexington to the Ky Horse Park.  That was quite a cool experience too!  We had a great week all in all.  We're already planning our next visit.