The organisation of the 1st Corps as given in Hindman’s Special Order No.51 dated 24th November 1862 shows Etter’s Battery assigned to Bradfute’s Brigade of four regiments of Texas Dismounted Cavalry.
In the Order of Battle for Prairie Grove, 7th December 1862, the same four regiments of Texas Dismounted Cavalry, together with Clark’s Missouri Infantry, comprised Roane’s Brigade. Artillery support was provided by Reid’s and Shoup’s Arkansas Batteries, both of which would prove to be temporary organisations.
(Shea, Fields of Blood p.292)
In the organisation of the 1st Corps in 12th December 1862, Etter’s Battery was still shown assigned to Bradfute’s Brigade, composed of the same four Texas regiments.
(OR Series 1, Volume 22, Part 1, p.903)
As you say, the question is where was Etter’s Battery during the Prairie Grove Campaign?
An examination of the CSR’s for the men of Etter’s Battery shows a company return for December 1862. Cards for various members of the battery indicate that they were at Little Rock from October to December 1862 (and probably into January 1863). Of the approximately 70 men listed in the battery, the December return shows 12 were either sick or had died and another 5 had deserted. 4 were assigned to wagon driving duties. 2 enlisted in the company that month. In addition a card for Lt. John C. Arnett states that he had left the company on the 4th December 1862 on recruiting duty. Putting this all together, this may indicate that the unit was struggling to have enough men to man the guns and that this was the reason the battery was left behind for the Prairie Grove campaign. This is supposition, but could be a likely scenario.