Wes--I'll take a stab at it as an native Texan (4 generations) now transplanted to Arkansas for 27 years. First a little geology and geography of the area:

The term "Ozark" is often misused. The "Ozark Plateau".. a geological "freak" between the Rocky Mountains and the Appalachins... are highlands, generally comprised of west-to-east ridges... that cover a good portion of W-NW Arkansas-parts of E-NE Oklahoma-SE Kansas-and a fair hunk of southern Missouri (think Branson, Springfield and Lake of the Ozarks). If you draw a line from about 30 miles northeast of Texarkana, paralleling I-30 to Little Rock, then on up to the NE corner of Arkansas (bisecting the state from SW to NE) you'll have the SE and Eastern extent of the Plateau.

Normally, in this neck of the woods, when we talk about the "Ozarks" we're talking to those mountains north of the Arkansas River (to further confuse, sometimes referred to as the "Boston Mountains"). The river bisects the state from Ft. Smith to Little Rock and feeds into the Misissippi about 90 miles south of Memphis. The "mountains" south of the river are generally called the "Ouachita Mountains" extending southward to Hot Springs-Mena and over into east-central Oklahoma.

Whether this "fine" distinction was made back in the 1860s, or not, (most probably "not") is possibly the basis of the "Battle of the Ozarks." It may well be that the Texas Reg. your ancestor was assigned to heard the locals referring to the hills ("mountains") of the Ouachitas to the west...and which possibly his outfit marched through...as "the Ozarks." If so, they may have, within their ranks, and in the lore and legend of the years that followed, referred to any battle fought along the way as "Battle of the Ozarks." I'm not sure at what point in history an "official" name is recognized by all parties as the defining name (see "Bull Run" vs "Manassas"...Yankees tended to name their actions after a geographical landmarks ...southerners after the nearest village or town, in many cases).

There were two major battles in the Ozarks in which Texas units played a large role...Pea Ridge (just below the Missouri border in NW AR) and Prairie Grove (a few miles west of present day Fayetteville). If his unit was involved in these battles, they may have simply lumped any and all "fights" in Arkansas as "Battle of the Ozarks."

If he's buried at Camden, south central Arkansas..piney woods and red clay hills.. he in all probability died in what is currently referred to as the Battle of Jenkins Ferry, or possibly, Battle of Poison Springs...or one of the numerous side-skirmishes that occured as the two armies fought over the area.

If you're interested in a follow up, there's a very active Civil War Round Table in Little Rock, and a Civil War in Arkansas webpage. I could try and check with one of their experts and see if they have any references to a "Battle of the Ozarks" in their files.