I think there was a Union 1st Ark. Cav. regimental history published by a fellow who used to be at the University of Arkansas. I can't remember his name here at work. If you check with the Univ. of Ark. in Fayetteville and/or the Arkansas Historical Commission, I think they can help you find the document.
My interest in the unit is because a distant cousin of mine (surname: Ledbetter) apparently was in the unit. Will check at home this weekend and see if I can find the history/author for you.
"Life is a bitch, then you die" - famous LA saying circa 1980s
Ken