It appears that Newton’s Arkansas Cavalry unit with him at the helm only appeared in 1863.

Outside the usual texts, the following books contain information on Arkansas' Civil War units may be of use:

Dougan, Michael B. Confederate Arkansas: The People and Policies of a Frontier State in Wartime. University, AL: U AL, 1976. 164 p.

Ferguson, John L., editor. Arkansas and the Civil War. Little Rock, AR: Pioneer, 1964. 364 p.

.....

Robert C. Newton
Enlisted as a 1st Lieutenant
"F" Co. AR 18th Infantry

…..

Robert C. Newton
Enlisted as a Colonel
Field & Staff AR 5th Cavalry

Sources used by Historical Data Systems, Inc.:
- Index to Compiled Confederate Military Service Records
- Field Officers, Regiments & Battalions of CS Army

…………………………………..

Robert C. Newton, 1st Lieutenant, Capt. William Reed’s Company (R), of the Battalion attached to 2nd Regiment Arkansas Volunteers,* enlisted July 27, 1861 at Chalk Bluff, Ark. by Wm. Reed for the war, traveled 35 miles to rendezvous, recorded present August 31, 1861, no further records

Note, there are no subsequent Company muster rolls in the records

* This company subsequently became Company F, 18th (Marmaduke’s) Regiment Arkansas Infantry

……………………………

The regiment went by a variety of unofficial names during its existence. When Colonel Robert Crittenden Newton was in command, it went by its official title of 5th Arkansas Cavalry. Colonel Newton was succeeded in December 1863 by Col. Thomas J. Morgan, formerly captain of Company C. Under Colonel Morgan's command, the regiment went by the designation 8th Arkansas Cavalry; but it was also known on occasion as the 2nd Arkansas Cavalry. The Compiled Service Records are filed under the designation 8th Arkansas Cavalry. The commanders of the 5th/2nd/8th Cavalry include Colonels Robert C. Newton, Thomas J. Morgan, and W. A. Bevens.
http://en.wikipedia.org/wiki/5th_Arkansas_Cavalry_Regiment

……………………

R. C. Newton, Colonel, 5th/8th Arkansas Cavalry,** receipted for one hat valued at $15.00, March 18, 1863 at Little Rock, Ark.

** He is shown on the 5th Arkansas Cavalry unit information card of the Field & Staff as Colonel of the 5th Arkansas only

This card notes: Newton’s 5th Arkansas Cavalry, afterward Morgan’s 2nd, also called 8th Arkansas Cavalry

His 2nd in Command, John W. Coreer Lt. Col./Lt. Col. was commissioned May 6, 1863, resigned July 18, 1863, 2nd Regiment Arkansas Cavalry

Thomas J. Morgan, Company C, Newton’s Regiment Arkansas Cavalry,*** enlisted January 10, 1863, at Pleasant Plains, Ark. for 3 years, promoted to Captain July 2, 1863, present at the Jul/Aug, 1863 muster, recorded on the 2nd Ark. Cav. Jan/Feb, 1864 muster roll as, promoted Colonel and transferred December 24, 1863, Hempstead Co., Ark., paroled May 11, 1865, Col. Morgan’s Regt.

* This regiment was designated at various times as Newton’s Regiment Arkansas Cavalry, Morgan’s Regiment Arkansas Cavalry, and 2nd Regiment Arkansas Cavalry; and at the same time it was known as 5th Regiment Arkansas Cavalry and 8th Regiment Arkansas Cavalry

M317: Compiled Service Records of Confederate Soldiers Who Served in Organizations from the State of Arkansas