I believe the so called dry wood laying around on the ground in the continuous rain, will most probably be soaked completely through to the center, after say the first week to month or so. I have been thinking to use the current fire to dry wood for the next fire by piling it around the fire you built. In general keeping it close but not close enough to burn. This would help the spitting and sputtering of the fire by keeping it contained. This dry wood would then be carried to the next encampment to help start the next fire. The rule would be don't burn all your dry wood at one place and time. I think wood chopped into slivers will dry faster than a log with the bark still protecting it.
Offered by Mike.
I would expect to be able to find plenty of wood for many years on downed tree branches being held above the ground so that they will just have been rained on. Most wood, even when immersed, takes several years to become "water logged". If it floats, there is still dry wood. After 20 years I would agree; but by this time I would hope there to be some vegetation, maybe even some trees that have adapted to the low light level. One would certainly want to always carry some absolutely dry material to initially start a fire; but remember, you are already pretty much loaded with the other things you are carrying. If all one needs to do is put out the current fire, just overturn the metal base so the remains are laying in the mud and use your entrenching tool to cover what's left with mud.
Offered by Ron.