If there's even the slightest chance of rain, the best precaution is to tape your muzzle, preventing rust as well as water buildup. A thin layer of tape over the muzzle will have absolutely no impact on accuracy.
I can't count the number of times that I've sat on a ridge, waiting for a bedded animal to move, constantly wiping my scope's lenses, but that isn't nearly as many times as I've stalked through sodden woods, stopping every few steps to clear the scope, running out of anything dry to clear it with. That said, I can honestly say that I have never lost a shot to a flooded scope, although I've certainly gotten wet plenty of times, and for darn sure I've worried about it often enough. It can happen, and it could have happened, so I've been lucky. Absent luck, use good scope caps, and learn how to use them quickly.
Understand one more thing: One of very few circumstances in the hunting world where iron sights are superior to scopes is during a hard rain. I'll go one step further: One of the few circumstances in the hunting world where open sights are superior to aperture sights is during a hard rain. Rain can collect in the aperture of a peep sight just as quickly as in the lenses of a scope and obscure it just as quickly.
The most common reason for a detachable scope backed up with iron sights is on a rifle that might be used for dangerous game. OK, that's valid. But I submit that the most compelling reason for a detachable scope is to give you additional options when it's raining, whether it's a sudden downpour or you're in wet country. Most of us cannot shoot as far, or as well, with iron sights as we can with scopes, but when it's raining, visibility is sharply limited anyway. Good old iron sights, properly zeroed, may well be a sound option, especially when you can't wipe fast enough to keep your lenses clear.
Accuracy is a more interesting issue. You will not shoot as well in a hard rain as on a lovely clear day, but there is little evidence that precipitation specifically interferes with a bullet's passage. Be careful with this. Visibility is clearly limited when it's raining, and you can't shoot better than you can see. At extreme range, as any artilleryman will tell you, humidity does affect the flight of projectiles. But no one shoots game at long range in a driving rain because you can't see to shoot in a driving rain. So if you can see it, you can probably shoot it without unusual adjustment. Maybe.
When I was a kid, I devoured the few hunting-related books in the school library. In one of J.A. Hunter's books (note: All of Hunter's books should be required reading) he told about closing on a really big elephant in a sudden shower. He passed on the shot because he was afraid the barrels of his double .500 were full of water and perhaps his shot would go high. Honest, guys, I don't have a clue where his shot might have gone, but I'm damn sure a barrel full of water is a very bad thing. At worst it will blow the gun. At best your shot will go somewhere.
If you think it even might rain, the best answer is to tape your muzzle. Electrician's tape is perfect, but any tape will do. Obviously, you don't want to block the barrel in any way, which means that putting a cork in the barrel is out of the question. But a thin layer of tape over the muzzle is not a hazard and will not impact accuracy. I've tried it--honest. The prevailing theory is that the jet of air pushed ahead of the bullet will clear the tape before the bullet ever arrives. Whatever, there is no appreciable affect on accuracy. On most hunts in mountains or forests where rain is likely I usually have enough sense to tape my muzzle. When I don't, I often regret it.
North American Whitetall North American Whitetail is designed for the serious trophy hunter. It provides authoritative coverage of world-class whitetails, the latest approaches to deer management and advanced hunting techniques.