Any wet wood can be made to burn as long as you get it hot enough. A forest that is tinder dry takes only a short time to be soaked in a good rain storm and then starting a fire can be troublesome. Having found myself in this situation several times I carry home made fire starters.
Take the portion of a paper egg carton that holds the eggs, fill the egg holding sections with relatively dry sawdust, pour melted wax over the sawdust till it is filled with wax and the paper egg carton is soaked with wax as well. These last forever and only require a dry match or a butane lighter to start. Once the wax has hardened break the units off from the main carton as needed.
Okay so the fire starter is burning now what to put on it as everything is wet? If there are pine trees around, take a few well needled branches from the tree, shake the water off, break off a bunch of the small branched clusters and place them on the burning fire starter. There will be some snapping and cracking but as soon as the surface water is gone the pine will burst into flame. Of course if you can locate a patch of pine pitch it burns even better (as indicated by earlier posts).
Being warm and dry is a blessing and can be a life saver and if nothing else you can cook that steak and potato you carried in when it was nice and sunny, once you have a nice fire going that is......63bkpkr

Oh, and thank you GSA for teaching me how to make these!