Both his Captain and Father stated that he died at Howard's Grove Hospital. I believe that his company had been assigned as Guards at Howard's Grove Hospital at the time as their later muster rolls indicate so. Muster rolls for 1862 do not exist.
How the American CW Database came up with Charlottesville is a mystery. This database frequently contains errors.
James M. Woodson, Private, (2nd) Company H, 46th Virginia Infantry, enlisted March 20, 1862 at Richmond, Va.,
Nov. 25 & 26, 1862, 1st Relief Guard 46th Va.
Dec. 14 & 15, 1862, 1st Relief Guard
Dec. 22 & 23, 1862, 1st Relief Guard
Dec. 27 & 28, 1862, 2nd Relief Guard
January 11/17[?], Richmond, Provost Marshall Office, Received of Sgt. John N. Hopkins one James M. Woodson of Co. H, 46th Va. Regt. who acknowledges to have deserted his command
January 17, 1862, Sgt. Hopkins paid $30 for the above apprehension
January 24, 1863, Pvt. Woodson admitted Howards Grove Hospital
January 24, 1863, Hos. Guard, Howard's Grove Hospital
January 28, 1863, Died Howard's Grove Hospital, Richmond, Va., Variola Conft.
February 28,1863, Company H was stationed at Howards Grove
April 30, 1863, Company H was stationed at Howard Grove Hospital
May 13, 1863, father B. H. Woodson filed claim for settlement of his accounts, Goochland County, Va., son died Howards Grove Hospital, Richmond
Aug. 17, 1863 Capt. Minor, Co. H. certifies Pvt. Woodson died at Howards Grove Hospital and was last paid 31 Dec., 62'
April 7,1864, Settlement No. 14,667, amount found due $21.32, CSA War Dept. Auditor
May 1?, 1864, Father paid
M324: Compiled Service Records of Confederate Soldiers Who Served in Organizations from the State of Virginia
I would believe he was buried in the Oakwood Confederate Cemetery, Richmond