I'm an infrequent poster here, but a lot of my posts have involved horses in the backcountry, simply because that is what I know. Both my wife's and my families have been in ranching in the west in three states for well over 100 years. Both my wife's and my grandpas supplied horses to the US Government for forest and land management, survey and various other tasks. In addition I've hunted off horseback all over the west of the US and Canada, in Patagonia, in the Urals and the highlands of Scotland for near 50 years...and, until I discovered these hunting boards on the internet had NEVER seen a scabbard low on the offside butt aft.

Read this:

Originally Posted by FLGator
The trailmax long range scabbard will accommodate a lot of modern and custom rifles, especially with scopes that dial. Hung on the off side, nearly vertical, muzzle slightly aft, off of the pommel will keep the rifle readily accessible, out of the way, not under your leg and keep the butt protected from tree trunks and most brush. I have noted excessive wear on the muzzle end of the scabbard from brush etc, but it works well in my limited experience


Then go to the Outfitter's Supply website linked a couple of times above and read this:
(FWIW Russ is a super good guy!)

Attaching a Rifle Scabbard, Bow Scabbard or Camp Tool Scabbard to your Saddle



The jist of this attachment is that you KEEP CONTROL OF THE HORSE, holding the reins in your left hand after you shuck the rifle and dismount.

I, personally, use the near exact hang slightly less aft canted, but on the ON side, balancing the load with a horn (pommel) bag to the off with all my possibles and water/lunch etc for when I'm in the saddle. Just a personal preference because I'd rather draw the rifle after I'm on terra firma...again, swing off the horse, maintain control with reins in left hand and reach up and shuck rifle with right.

With the offside, near horizontal hang some of y'all use, how do you control the horse as you go to the kicking, bucking end on a tight trail, near vertical with a skittish mount to draw the rifle?

You can no more tell someone how to do something you've never done, than you can come back from somewhere you've never been...