Corrected entry: The characters are shown entering a large desert. When they stop at the cave, they light a fire with wood. The desert hasn't got any vegetation at all.
Corrected entry: When Jet Li, Jackie, the Sparrow and the kid are going into the desert, it's obvious that they are walking deep into it. When they stop at the cave, they light a fire with wood. The desert has no vegetation and carrying it for such a large distance seems very impractical.
Correction: Deserts can get extremely cold at night, so a fire is something of a necessity. Carrying wood in order to make said fire may not be the most practical thing in the world, but it beats freezing yourself into unconsciousness hands down.
Correction: Sorry, that's just wrong. Deserts have an amazing range of vegetation and wildlife. People in the Middle East have been surviving for millennia as nomads in the desert, and they do burn wood in addition to camel dung.