Quote Originally Posted by MeatMarket View Post
I'd say it might be an improvised attachment by the soldier on horseback. The soldier in the first picture probably has his hanging from the flap of his M1910 or M1928 haversack. There are two grommets on the top right side of the main flap to hang it from and a loop at the bottom to keep it from flapping around.
Yes, the M1910 & M1938 packs had grommets to attach such items as the bayonet frog.
BUT
The text below the first drawing that you refer to states that the scabbard is attached to the cartridge straps!

Given that the OP is referring to a Cavalry unit, and such units had personnel called Saddlers...I'd have a SWAG that one of the unit saddlers added a few leather or canvas loops to the standard M1936 suspenders to allow the bayonet scabbard to be carried as shown in the 2 drawings.