Peter Kummerfeldt just addressed this in his blog:
  Outdoor Safe Blog Another option I have used in very wet environments is a railroad flare.
I have also carried tinder and kindling inside my clothes to dry it. 
[/b]
Cutting into the center of larger pieces of wood will remove the wet outside.  I do not agree with this advice. I specificly disagree with this advice because it is incomplete.
Cotton wool balls make a good, easy to use firestarter. However  [b] 
they are not sustained flame.       Substained flame    means a firestarter that burns hot for several minuites. In practice that means Esbit, Wetfire, barbeque firelighters or the like.
I very strongly suggest that anyone reading this thread reference "David Canterbury" and/or "Wilderness Outfitters" on YouTube. 
You will find that an eye opener.