Yes, it is possible to go WWOOFing as a family. Note that each adult must sign up as a WWOOFer (in most countries it is possible to sign up with a joint account) while children under 18 do not need a WWOOF membership.
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.