I'm always moving through some really rough country, rather than sitting. It's one thing to keep your lock under a coat flap and the muzzle pointed down while sitting, but another when you have to move, often using one or both hands for scrambling. I find the simplest muzzle cover to be modern electrical tape, while the lock is best covered with a cows knee.
I made mine from a scrap of chap leather, and cinching it down with the bottom tie pulls the front and rear down tight to prevent water running along the rifle and into the lock. Took a little adjusting to get that seal, but I was rewarded in the end. BTW- When I say cinching, that deserves an explanation. I punched a 3/16" hole in each side below the trigger guard, and I pass a 1/2" wide tie through those. There's enough friction without a knot to hold it in place. But with a single overhand knot it's really secure, but I can pull it off easily with a single jerk. Handy, effective and quick.