I can't find any record of subsequent service of William H. Giddings, at least in any Arkansas regiments, Confederate or Union.

Col. William Ferguson Slemons, commanding officer of the 2nd Arkansas Cavalry, was highly thought of by his men, despite being a strict disciplinarian. I've been going through a box of my old research papers and found several transcriptions I had made years ago, regarding courts-martial ordered by Colonel Slemons. The regimental courts he appointed were tough--Pvt. N. B. Holland was drummed out of the service for killing a hog; Pvt. W. H. Giddings was drummed out of the service for stealing a gold locket; etc., etc. Several men were sentenced to ball-and-chain. Despite (or because of) the strict discipline, Colonel Slemons was a popular commander, and his regiment was considered to be one of Arkansas' premier cavalry regiments.