I have found the records, which raised a few more questions than answers. :)

David C. Wolfe enlisted in the 4th Arkansas "Mounted" Infantry on January 25th, 1864.

But here is where it get muddled. He enlisted along with his brother on the same day, John D. Wolfe who was captured in Sept. 1863 and sent to Camp Douglas MP, IL. while in the 6th Arkansas Infantry(C.S.A). So either he joined up with the Union, or swore allegiance. Or I might have faulty info.