Barbara,

Here is a little info. for you, and yes he did serve in this unit.
You really need to get this soldier's records to see what happened to him in the war. You can do that at this web site.

http://history-sites.com/research/index.html

Private B. (Barzelia) Hayter of Company I Texas 2nd Cavalry Regiment, Partisan Rangers.
Organized in early 1863.Dismounted in Feb. 1865.
Surendered by General E. K. Smith ,Commanding Tran-Missippi Dept. on May 26, 1865.

Commander: Colonel B. Warren Stone
Field Offercers: LT. Colonel Isham Chisum
LT. Colonel Crill Miller
Major James W. Throckmorton
Major James G. Vance

Battles:
Donaldsonville - June 28, 1863
Stirling's Plantation (In reserve) - Sept. 29, 1863
Bayou Bourbeau - November 3rd 1863
Red River Campaign - March-May 1863
Mansfield - April 8, 1864
Pleasant Hill - April 9, 1864

I hope this helps you,
Gary D. Bray