At the fall shoot in 1974 on the primitive range at Friendship, my best buddy got all geared up to shoot even though it looked like it was going to rain badly. His repro pre-Rev War rifle had (and still has) a loop in the trigger guard and a sling. (The builder of the rifle must not have known about adding a barrel lug on the 42" swamped barrel for the sling. I expect the builder just copied the rear sling swivel from a book. Anyway, the sling wrapped around the barrel in front and it never got in my buddy's way during shooting.) Then the rain clouds opened up and poured water down on everyone. My buddy slung his rifle upside down on his right shoulder and even though he is only about 5'6", the muzzle didn't come close to touching the ground. Water poured down his hat, his buckskings, his shooting pouch, etc. in what looked like small streams. He stayed until he looked like a drowned rat and no one else came up to shoot that morning. He finally looked at the gent running the match and told him he thought it might be best to cancel that day. I still kid him he looked so pathetic and forelorn that day. Grin.
Slings were common on Brown Bess muskets even when the barrels were still 46" long and before the "short land" pattern barrels of 42" length became the norm. However, since there is nothing in most period drill manuals about "sling arms" as a drill movement, conjecture is that they slung the muskets across their backs with the butts over their right shoulder and the muzzle going down their left side. The use of the sling most likely was rare, even by the military. Maybe only in the rain to keep water out of the barrel as best they could and when they had to traverse difficult terrain. Maybe also when they were on some work details where they had to keep their musket close to hand, but while keeping their hands free to work.