Here is a link to the topic Steve mentioned. Read the last few posts.
K12 logging tractor - #7 by madflower69?
The biggest problem with burning wet wood is not really the extra tar and soot in the gas, but the fact that the reaction not going to get hot enough. Sure it would still work and it would still be making gas but the heat loss from all that moisture will reduce the volume of gas and efficiency of the reaction.
If it were me I would look into making a charcoal retort like Matt has done. And then build a charcoal gasifier to create the required wood gas. That way you could still the wet wood only running the vented gas back into the reaction to help substitute a percentage of the heat required to convert the charcoal.
Anyway just an idea…