....Moisture? They certantly don't need moisture and fly line is nothing like dacron backing.
Robert I've used my fly line in some pretty harsh conditions (winter) and don't believe cold will bother the line what so ever. What you will find though is the line becomes quite coily after sitting on the reel over time. This is no biggy just un spool it in the new season and give it a gentle stretch. The rest of your gear should not be affected by the cold either (fishing isn't just a hot weather sport), but be sure to put it in a safe place where it won't get knocked around and do not to store in a manner that can warp the rod and never store it in the same room as your furnace.