Children are part of the stories in This War of Mine, however their presence and involvement with the story is greater with The Little Ones DLC.
Children always seek for mood boosters. When idle, children will go play around the shelter. looking for something or someone to play with. They can easily get depressed, but also get entertained easily. Children needs less food than adults, only eat one meal for every 3 days. At first they don't have any skill to do things normally done by adults, but they can be taught to do things like cooking or setting animal traps. But they hates doing work, and doing it too much would make them sad.
At night, children cannot scavenge or guard. They also unable to guard the shelter from the looters at all, even during sleep. So the looters will steal things unopposed and children will get sad when it happen.