We hunted off of mules/horses, three-man team or a four man team.
With a horse/mule carrying your gun, I do not see the need in having an ultra-light rifle. None of us in our party even thought about the need for an ultralight. Two guys hunted with BAR 7 Mag with the Boss which was tuned to be extremely accurate, and I hunted with a Browning Stainless stalker in 7 Mag which grouped 3/8". We saw our hits with 140g Partitions due to brakes. We never shot within 100 feet of the mules, and shots were away from the mules. A fourth hunting partner hunted with a 257 Weatherby using Weatherby 117g Factory ammo that just flatten elk in their tracks, the boy could shoot, and he had a brake also.
The shooting was a planned event, with the safety of the other men and mules being a priority. We hunted the roughest country you could imagine.
It would have to be a thin can to get the darn thing in and out of the scabbard. None in our party would ever wear his rifle slung over his shoulder while riding a horse/mule.
Again, I question the need and the value of having an ultra-light for horseback hunting, but guys do hunt very differently.