Wet wood... yes it is a problem. And the only answers I have add to
the weight that you carry with you. The least desirable (weight wise)
is a tool to split wood. Inner wood of a branch is usually dryer...
even after multiple days of rain.
There are several "fire starters" that can be used; Small piece of a
candle. Cotton balls saturated in petroleum jelly (Vaseline) or even
high alcohol content waterless hand cleaner. There are also several
different kinds of commercial products, like Esbit tablets, that can be
used. Even if you don't bring along the alcohol stove, a small amount
of alcohol helps to get a fire going.
All will take very good fire starting skills, ie; starting with very
small match stick sized pieces and working up to larger dia. The key
point is being able to keep increasing the size of the fire so that the
heat from the fire can be used to dry increasingly large pieces of
wood. Once you have a fire established it's easy to dry wood. But
there in lies the problem... getting the fire started.
djl