While I've never had to start a fire under thoise conditions, it should be possible, provided you have the proper "ingredients". First off, I'd make sure I always carried good tinder as part of my firekit. I have 3 ounces or so of finely shredded Juniper bark, 8 3x1 inch pieces of fatwood, char cloth, and lots of cotton balls, both with and without candle wax dripped on them. Having this on hand will prevent me from having to find dry tinder. To light it all, I have either strike anywhere matches, 2 or 3 Bic type lighters, and a large ferro rod with striker.
Now you'd need to get dry wood. If you don't have a large knife or hatchet to split wood, you're going to have to really dig around trying to find some reasonbly dry wood to use. Around here we have lots of dead lower branches on Junipers and pines. The canopy above should keep those limbs dry enough to get going with my dry tinder. Once I get a fire going, under a tree for shelter (not so close as to pose a fire hazard), I would use the heat from the fire to dry out more wood.