In my limited experience the level of humidity has some effect, but not enough to really matter much. It's still a matter of hours - not days!
This past winter I shot a deer in the rain and didn't re-load or wipe the bore. I had the deer field dressed, tagged, and in the processor's cooler within a couple hours at most. As soon as I got home I cleaned the rifle and there was the brown color of rust on the first patch through the bore. No damage, but it was already starting to form!!!!!!!!!
In low humidity conditions you should be good for a few hours, but I always figure the sooner the better for cleaning!!!!!!!!