Mike -- Several years ago I ran across a postwar list of members of Etter's Arkansas Battery (the Washington Artillery, of Hempstead County). It may have been prepared for a veterans reunion. Willoughby Smith was listed as a member of the battery.
There's no way of verifying his service (or most others on that list) because contemporary records of Etter's Battery are almost non-existant. I found a copy of an early roster (or report of detailed soldiers), but not much else.