I am going to guess this is a percussion cap model rifle and work from there...

Duct tape over the end of the barrel will work to keep the moisture out. If you don't like duct tape, plastic wrap and a rubber band works. Condoms work. I have even seen balloons used. I use finger cots. Go to Wal Mart and get a box of the extra large ones. A finger cot is a latex finger that you roll over a finger with say a cut to keep it extra clean and dry. They do stretch a little and you might want to practice, but they will go over the end of the barrel. Just not over the sight. They also sell muzzle mits. Which are finger cots at an inflated price. They will stretch also. Or you can keep the muzzle pointed at the ground as you walk and as you stand or in stand and only raise it up when your ready to shoot. All we are trying to do is to keep rain and snow from going down the barrel.

On the cap end... a tire valve stem cover will go right over that capped nipple and then you can lower the hammer down on it. This acts as a great safety and it keeps moisture off the cap. I used to carry a birthday candle. And I would rub the edge of the cap with it to seal it in wax. That also keeps it dry.

But the most important part is prepare the rifle correctly before you go hunting. Before you load.. run an alcohol patch down the bore of the rifle to remove the oil in there. Then a couple of dry patches. Now push a dry patch down on a jag to the bottom of the breech, cap the rifle only, and fire the cap. Pull that patch and check for burn marks. No burn marks? Do it again. Do it until the patch has a good solid ring of black burn mark. Then I like to pop one more cap through the gun with the muzzle pointed at say a piece of dirt on the floor. If that gun is ready to load, it will blow that dirt away from just the power of the cap.

Now you know the barrel is dry, and the flame is going through the bolster/drum into the fire chamber. So you can load the rifle and have a great confidence that when it comes time to pull that trigger.. that gun will fire.