Yeah, without dry tinder you're going to have problems, so it's worth keeping a stash in a ziplock. Also, humidity makes a big difference. Here in the northwest you have to worry not only about the water in the wood, but also in the air and in the ground. You always want to scrape down to dry soil, or build on a flat stone, tin foil, dry side of a small board or something. Otherwise you'll see the steam come up from the ground and put your fire out before it gets started.
Also don't be afraid to get creative about tinder. Although it's not PC, adding small pieces of plastic, styrofoam, dried orange peel etc. to get a flash of heat can make all the difference. Same with spreading a little oil or grease on the wood. Another thing that works great for tinder is those little bags of snack chips. They're greasy and they're always dry. Alcohol, diesel, wax, kerosene are all good, but be careful of gas and gunpowder. The guys in the tropics use little squares of innertube. Don't breathe the smoke, but your fire WILL start! This is probably more than you'll need for a dewy morning, but hey, it's always good have options, right?
Once your fire is started, keep the damp wood on the side to warm and add it just a little at a time, or the steam can quench your fire as it heats up.