If an overly saturated cotton ball is difficult to ignite, you can bring along an unsaturated cotton ball, lint or anything else that will catch a spark easily. Ignite that clean cotton ball/lint right next to the (possibly) overly saturated cotton ball. This may sound more complicated than it really is. I recommend experimenting once.

I like cotton balls mixed with PJ because it's nearly idiot-proof. It doesn't tax my fine motor skills. What I like perhaps even better is cotton balls mixed with Burt's Beeswax lip balm.

Even better than these is a candle-in-a-can which can be ignited multiple times to start a fire (e.g., to get kindling going). To get the wick on the candle going, you will need some shelter (to keep the rain off), dry cotton and a flint. Or, instead of the dry cotton and flint, just use a lighter to get the wick going.