Might have found the elusive 1920's manual, but it's not 1920's. It might first have been 1920's. It is still out of print, but apparently was reprinted as late as 1979. Same name (almost) and reads as if it might be the manual in question "U.S. Cavalry Manual of Horse Management" is the manual in question and this is "Cavalry Manual of Horse Management". Still came out of Ft. Riley and used during the time between WWI and WWII, so it might be the same. 1920 was shortly after WWI.
You can get a general look at it. Check this link and see what you think. Cavalry Manual Of Horse Management By Editor-Frederick L. Devereux - Used Books - Hardcover - 1979 - from Gadzooks Books and Biblio.com