Jesse was killed during the Battle of the Wilderness. His body was initally buried on the battlefield near Orange Plank Road by his captain, Jonas Lipps. Even though Jonas marked the grave and knew where it was, Lipps was captured before any formal marking (a tombstone)could be done for the gravesite.

Eventually, Jesse's body was removed, along with other fallen Confederate soldiers, to the cemetery in Fredricksburg and buried in a mass grave.

Jesse had, shortly before his death, announced in a letter to the Wise County paper, his intention to be on the ballot of the upcoming election for Wise County as Commissioner of Revenue.

According to an account by Jonas Lipps:
May 5, 1864: Taken up the line of march at day break and engaged the enemy at the Battle of the Wilderness at about 2 o'clock and Gen. Jones was killed and I witnessed his remains appearance.
May 6, 1864: Lay in line of battle and fortified, and skirmished with the enemy, and burried Jesse Horn, and marked his grave.
May 7, 1864: Lay in line of battle in the breast works till about 10 o'clock. Taken the line of march to the extreme left of the general base fighting continually along the line. The dead were burried today. I showed D. P., J. H.'s grave.
http://www.rootsweb.ancestry.com/~vaslcudc/JonasLipps.html

The material below was supplied by Gary Wade, a retired Colonel of Company D reenactment group.

Enlisted at age 34 at the Wise County Courthouse in Company H 06/03/1861

In hospital White Sulfer Springs (Now West Virginia) 08/20/1861-11/01/1861 The 50th had a measles outbreak that left them about 3 companys short about this time.

Killed In action 05/05/1864 at the Wilderness.

Buried by his Captian Jonas A. Lipps marking the grave 5/6/64

Lt. Col. Gary L. Wade
50th Va. Co. D
retired

(Material from Findagrave.com)