Yes, it is possible to go WWOOFing with children. Note that each adult must sign up as a WWOOFer (with an individual account if you are the only adult traveling or with dual account if you are two adults traveling together). Children under 18 do not need a WWOOF membership, when accompanied by a parent or legal guardian.
Please also note that children are not covered under automatic insurance (if offered), and parents are responsible for ensuring their children are covered.
Some hosts accept children and others don't (as is indicated on their profile). Always check with the host first, and if you have young children who need a lot of your attention, please discuss this with your host. Farms can be dangerous places, and accommodation can be limited. Parents should be willing to take total responsibility for the safety of their children.