Lynn ,
Yes, the shorter strap has a U hook attached to the belt ring . I did a quick search of Spanish American war saber belts for re-enactors, as the 1860 model was changed slightly , by 1870.
Heres the link , They also show the Vol belt buckel.
19th century leathergoods, belts
The back strap looks to be about 16 inches, this would make practical as the Military had reverted to using set standards for horse height.
Short to the front , long to the back of the saber. When mounted the saber hangs free, to allow for the movement of the horse and to allow the saber to swing freely away from the horses legs. A hooked saber when mounted has a tendency to roll under the horse putting the saber betweeen the horses legs. If that happens , can we say rodeo ?
A floating saber will stay out from the horse legs as the strap will follow the curve of the horse placing the saber to the outside of the leg.
If you remember the movie Shenandoah , (with Jimmy Steward) there is a scene where two bums come to the well for water, one has a saber hanging down to his side. Remember the effect of the saber clanging as he went up the steps...
Great movie effect , but stupid and not likely , the saber scabbard has a enlarged section at the base of the scabbard , it is called a drag . This drag is designed for just that , to protect the scabbard from dragging the ground.
If it does drag the ground , it will cut a path in the dirt to roughly follow who ever is dragging it. The issuse becomes it inpeads motion. If you turn , it will trip you, if you try to back up it will block you, and if someone is behind you in formation they can and quite often do step on them , again jerking you at the waist , usally causing you to lose balance.
The scabbard is made with an end that locks the sword into the scabbard , some even contain screws. That is why in the manuals the command to draw sabers is given as a two part movement. At the command draw , the saber hilt is pulled out of the scabbard , to do this some of the sabers were so tight it could take both hands to pull it to free the hilt. It is not possible to free a saber quietly from a scabbard, as you free the hilt the saber will rub the scabbard.
The curve is the main difference between a sword and a saber. The cavalry saber curve is designed to at the charge be placed alongside the neck of the horse point to the center of the neck , then before impact to turn the pont in the direction of impact to allow the motion of the arm to maintain contol of the movement. As the rider moves forward the saber will pull free of the point of impact where it can again be return to placement along side the horses neck.
Well there I go rambleing
Ash