There was a William D. Williams who served in Co. F, 3rd Arkansas Infantry; and a William D. Williams who served in Co. G, 3rd Arkansas Cavalry.
The man who served in Co. F, 3rd Arkansas Infantry, died of disease at Fredericksburg, Virginia, on December 10, 1861.
The man who served in Co. G, 3rd Arkansas Cavalry, was severely wounded in a skirmish near Franklin, Tennessee, on June 4, 1863. He was left behind and later captured on June 12, 1863, and spent the rest of the war a POW -- released from Fort Delaware on May 30, 1865.