I hunt a ton with horses so with that being said I've ridden all my life and spend majority of my time in the high country on horses/mules.
We usually hike from our base camp but if we are riding its not too far and its just to tie off and start hiking. My buddies and I all carry our bows in our hands and if you get tired we place the lower limb on the top of our boot. Some of my buddies are extreme novice horseback riders so I give them their bow once they are mounted. We've had our fair share of wrecks and if it was a bad one we would just toss our bows off to the side. The damage from the toss is no more than a bow in the scabbard on a horse/mule crashing into trees, pack string, and/or rolling over.
I would definatley use some of these scabbards listed they look awesome and well worth the investment and safety.
I should also note this is usually how we carry our bows after we reach campe and just riding to hunting/hiking spots. if I'm leading a packstring in I take my longbow down (I shoot all 3pc longbows) and throw it on a pack horse/mule.
Good luck
James