Here is what Russ Barnett, founder and owner of Outfitters Supply, recommends:
I personally hang my rifle scabbard on the off-side of the horse. I attach it with the rifle butt toward the front at about horn height, and angle the rifle barrel slightly toward the back.
Here's why:
The barrel of the rifle extends under my stirrup leather and I never know it's there.
This keeps the weight on the front quarters of the horse where he can carry it best.
On the off chance I should spot game while in the saddle, I can pull my rifle out before I dismount.
Hanging the shotgun scabbard or rifle scabbard on the off-side can help offset your weight when mounting.
One additional note, if you use an open ended leather or nylon rifle scabbard and hang it with the butt toward the rear, your rifle could end up missing. I have heard many stories where folks have found their rifle way back on the trail because they never knew it had been snagged on a branch and yanked out of the gun scabbard.
