There's a reason (some) women put on more makeup when they're going on a job interview or a first date—and those neat-looking black stripes under football players' eyes are more effective at looking awesome than guarding against the sun.
Jack (duh) is the first one to pretty himself up, and he does it because he figures out that his pig-prey keeps spotting him: "They see me, I think," he says: "Something pink, under the trees" (4.2). And so he gets the bright idea to paint his face, "dazzle paint. Like things trying to look like something else" (4.24).
But the paint turns out to be more than camouflage. It doesn't just make Jack look like something else (say, part of the forest); it actually makes him into something else. It makes him into a savage—and then the chief. When his face is finished, "the mask was a thing of its own, behind which Jack hid, liberated from shame and self-consciousness" (4.34). With the paint on his face, Jack isn't choir-leader Jack anymore; he's a savage ready to be chief.
And Jack isn't the only one who has an inner savage. Eventually almost all the boys paint their faces, too. Ralph and his tiny band of still-civilized boys know that it's just paint, but that doesn't change its power. When they plan to go take Piggy's glasses back from Jack, Eric hesitates: "But they'll be painted! You know how it is." And everyone does: "They understand only too well the liberation into savagery that the concealing paint brought" (11.66).
So there you have it. Golding isn't being tricky with this symbol; paint "liberates" the boys into savagery, freeing them to act in a way that schools, parents, and policemen have never let them. In other words, the paint represents the savage within. It doesn't disguise the boys' true nature; it reveals it.