Starting a quick list of references to the state of the U.S. cavalry's horses in 1864.
Sherman mentions the difficulty of getting horses; suggests mounting the best men and using the remaining cavalry as dismounted cavalry.
Official Records, Series 1, Volume 32, Part 3, (271-272, Sherman to Thomas), 272.
Official Records, Series 1, Volume 32, Part 3, 406-407.
Suggestion for Solving Cavalry's Horse Problem
Grierson to Thomas, April 18, 1864.
Suggestion for setting price for northern horses and impressing horses if citizens won't accept the price. Mount all men in unit or else dismount and train them as infantry.
The War of the Rebellion: A Compilation of the Official Records of the Union And Confederate Armies. Series 1, Volume 32, In Three Parts. Part 3, Correspondence, etc.