Are you wanting to hunt from horseback or simply transport your weapon on horseback? Ravin offers a soft case with built in backpack straps.
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Will want to have it on a horse both uncocked and cocked. I wouldn't hunt from the horse, but would for sure want to be able to jump off and head after elk without cocking. I really wouldn't want it on my back on the horse, you don't want any extra weight on your back to mess up your balance in the mountains or anything that branches can grab to help you off the horse. I'd be riding with a pack but with as little in it as possible.