First of all the question arises of, How did your husband determine that this cemetery was a "Confederate" cemetery?
Most likely it was because of Confederate Veterns tombstones placed on the graves. There are many such cemetery throughout southern Arkansas which are commonly called "Confederate Cemetery" because of the headstones within them. However almost all of these cemetery are post-war burials.
In Arkansas almost every able bodied man was enlisted at one time or the other in the Confederate Army especially in south Arkansas because of the conscription laws in the Confederacy. Therefore every old cemetery in south Arkansas whether a private family, or church, or public cemetery will have many Confederate Veterans buried in it whether the graves are identified as such or not. Confederate Veterans Tombstone were not available until after the 1900's and many have been placed on veterans graves since the 1950's by the United Daughters of the Confederacy and the Sons of Confederate Veterans. Aiding familys to identify the service of a Confederate Soldier and helping the family to obtain a tombstone for that grave is one of the missions of both these organizations.
I would suggest that you contact the Bradley County Historical Museum in Warren. They may know of the cemetery you speak of. Mr. Tim Johnson, recently deceased, was a worker at the facility and was very involved in Civil War preservation and may have left information with the Museum which could aid you. Also if you are interested in Civil War preservation in Warren I would suggest that you contact Mr. Bill Farmer, who is the new postmaster in the Warren Post Office.