If you're going to expose the rifle to drastic temperature changes, take off the tape and let the barrel air out. Wipe the metal down with an oily rag at the end of the day. Pay particular attention to the bolt, which is bright metal and prone to rust. If you're hunting in a dry climate, such as in the Rockies, rust doesn't seem to occur, no matter what the weather is. But elsewhere, beware.
Triggers are especially vulnerable.
I've seen at least a couple that were ruined by rust from being wet day after day. The cure for this is to put a little bit of light, Teflon-based oil on the sear. Do not slather the trigger with oil that can congeal in cold weather, or you will find yourself with a rifle that will not cock. Another cure is to shoot a squirt of lighter fluid through the trigger after each soaking. This appears to lubricate it just enough so that rust doesn't form.