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 generally do not need a WWOOF membership, when accompanied by a parent or legal guardian. However, in some countries the rules for minors might be different, so please check out the membership terms of your national WWOOF organisation.
Please also note that children may or may not be covered by the automatic insurance, if offered, depending on the country. Parents are responsible for ensuring their children have appropriate insurance coverage, so please check with your national WWOOF organisation to confirm whether children are included.
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.