I believe the 4th was in camp at a place called Camp Furgeson when G. W. died. Had he died in battle, I would have suspected this would have been so noted, or perhaps having died of wounds received in battle. In-as-much as 10 men are recorded as having died of wounds received at Pea Ridge/Elkhorn Tavern, he may have been one of these men.

Following Pea Ridge, the next engagement they are recorded as taking part was that at Richmond, Ky Aug. 29/30, 1862

4th's Battles State Date Casualties

Elkhorn AR Mar 7, 8 1862 K5,W36,M14,DW10
Richmond KY Aug 31 1862 K4,W14,DW3
http://www.rootsweb.ancestry.com/~armontgo/fourth.htm

B F. Howard, discharged February 20, 1863 due to gunshot wound in the left arm, age 22, born in Missouri, Farmer

G W. Howard enlisted as a Private in Company H, 4th Arkansas Infantry, January 9, 1862 at Dallas, Arkansas, died June 15, 1862

Isaac Howard enlisted as a Private January 13, 1863 at Dallas, Arkansas, shown present on July/August 1864 muster, no further records

William M. Howard enlisted as a Private in Captain Earp's Company, South Arkansas Regiment, subsequently Company H, 4th Arkansas Infantry, on August 17, 1861 at Camp Etter near Mt. Vernon/Miller Spring, Missouri, furloughed sick October 5, 1861 to March 1, 1862, promoted to 2nd Corporal, later to 1st Corporal, shown present on July/August 1864 muster, shown on a receipt roll for clothing September 30, 1864, no further records

all enlisted as Privates
"H" Co. AR 4th Infantry

The Fourth Arkansas infantry was organized at Miller's
Springs, Lawrence county, Mo., August 17, 1861, by the
election of Col. Evander McNair, of Hempstead county;
Lieut. -Col. A. Bryce Williams, of Hempstead county;
Maj. J. H. Clay, of Montgomery county. The regiment
was reorganized at Corinth, Miss., May 8, 1862. The
companies were commanded as follows : Company A, of
Calhoun county, Capt. Joseph B. McCulloch, succeeded
by First Lieut. George Eberhart, Second Lieut. Wiley C.
Brown, Third Lieut. H. G. Bunn (who afterward became
major, lieutenant-colonel and colonel of the regiment).
Company B, of Hempstead county, Capt. Rufus K. Gar-
land, elected to the Confederate Congress and succeeded
by First Lieut. Henry J. Bonner, Second Lieut. J. W.
Paup, Third Lieut. John L. Loudermilk; Henry J. Bon-
ner, made captain at the reorganization. Company C, of
Montgomery county, Capt. F. J. Erwin, First Lieut.
Nathaniel Grant, Second Lieut. J. Scott, Third Lieut. J.
Bates. Company D, of LaFayette county, Capt. Joseph
C. Tyson, First Lieut. Charles A. Jenkins, Second Lieut.
James M. Meyers, Third Lieut. Chesley G. Williams;
on reorganization Samuel W. Mays was made captain.
Company E, of Hempstead county, Capt. John A. Rowles,
First Lieut. Samuel Ogden, Second Lieut. Augustus Kyle,
Third Lieut. Ellis G. Winstead; on reorganization
Augustus Kyle was made captain. Company F, of Mont-
gomery, Capt. J. M. Simpson, First Lieut. J. W. Laven-
der, Second Lieut. Arthur Mayberry, Third Lieut. P. D.
Davis; Captain Simpson was mortally wounded in the
battle of Elkhorn, and First Lieut. J. W. Lavender be-
came captain. Company G, of Pike county, Capt. James
F. Black, First Lieut. William B. Gould, Second Lieut.
John N. McCollum, Third Lieut. H. Clay Polk; on reor-
ganization W. B. Gould became captain. Company H,
of Polk county, Capt. William H. Earp, First Lieut.
James M. Helton, Second Lieut. F. M. Bolin, Third
Lieut. Josiah Earp. Company I, of Polk county, Capt.
Joseph B. Williamson, First Lieut. Caleb Cox, Second
Lieut. George W. Mason, Third Lieut. George W. Walker;
on reorganization J. W. Blackburn, of Benton county,
became captain. Company K, of Calhoun county, Capt.
0. H. Black, First Lieut. Joseph Wilmon, Second Lieut.
A. W. Land, Third Lieut. Peter Johnson; on reorganiza-
tion Thomas A. Smith became captain.

The regiment participated in the battles of Elkhorn,
Richmond, Ky., Murfreesboro, Jackson, Miss., Chicka-
mauga, Resaca, New Hope Church, Kenesaw Mountain,
Dug Gap, Peachtree Creek, Atlanta, Ezra Church, Love-
joy's Station, Jonesboro, Franklin, Nashville, Sugar
Creek, and Bentonville, the last prominent battle of the
war. This regiment early won distinction in the com-
mand of the gallant Ben McCulloch. Its colonel, Evander
McNair, was promoted to brigadier-general and earned
enviable fame early in the war.

Source: Confederate Military History, vol. XIV, p. 287

For further information, see: http://www.couchgenweb.com/civilwar/4mcnair_indx.html