The standard emergency tinder in most places I have been is a lichen called Old Man's Beard. It can appear in several forms. Here are the first two from Wikipedia:
Even if it is soaking wet, heavily raining, caked in ice, or encased in snow, one need only remove most of the excess moisture by vigorously shaking (or bending to break out the ice). It is then readily used as tinder. Of course the drier it is, the better; a little moisture retards its flammability.
If you carry white gas as fuel for a portable stove, that makes an excellent "dryer" for wet materials (even paper) and makes the tinder easier to ignite. Be sure to expect a small fireball as the fuel vapor will travel a few feet.