There are two possibilities on finding out how a regiment was equipped. The first is the Compiled Service Records (CSRs) and the second is the Quarterly Ordnance Reports.
The CSRs often how very valuable research material often overlooked or not looked at all. When you look at the CSRs, look at the officers in the companies, the Field and Staff officers, the brigade officers and staff records. These records will often have issue and turn-in documents and I have found several quarterly ordnance reports too. The brigade officers and staff records can be found at the National Archives in Washington, D.C., Wallace State College in Hanceville, Alabama, or the Birmingham Public Library. I am not sure if the National Archives Annex in Atlanta has them. I believe the Chattanooga Public Library is scheduled to purchase them but I do not know if they have done so yet.
The Quarterly Ordnance Reports that did survive can be found at the National Archives in Washington, D.C. Again, I do not know what the Annex in Atlanta has available.
The weapons that were available and issued throughout the war varied. Cavalry regiments often started out with nothing more than personal shotguns, pikes, and sabers then evolved to carbines while ditching the pikes and sabers.
Horses were issued but often the soldier was responsible on keeping himself mounted. I have seen several accounts that if the cavalryman could not remount himself then he was transferred to the infantry.
I have seen a standardized lists of equipment that a cavalryman was expected to have in his possession and to maintain.
I hope this helps in you search.
Gerald D. Hodge, Jr.
War Between the States Historian
Historian: 39th Georgia Infantry Regiment
Web Master: http://39thGAVOLINFRGT.homestead.com/39thHomepage.html