There's 2 types of wetness for logs, what I call surface wetness caused by it being rained on for example and there's internal moisture saused by lack of seasoning.
It'll be harder to burn in either case. In the first case, a day or so in the house next to the burner should dry it out enough, if its the latter then you risk sending stuff up the chimney that can cause tar/soot build ups. Burning any wet-wood also sends steam up the chimney that can also cause soot buildup.
For seasoning wood, in my experience, adequate airflow is more important than storing wood in a waterproof room.