For: The crucial first step in embarking on a walk with children is to sell the idea properly. Tell them you are going out on foot to promote good health and exercise and they will laugh in your face and refuse outright to shift from the sofa. Package it, on the other hand, as an incentive-driven, goal-oriented proposition and they will be more likely to cooperate. Once you have ignited their interest, you will need to work like stink at following through with lavish promises of limitless muddy puddles, big sticks, endless processions of fascinating agricultural vehicles and, God willing, sundry bloodied and mangled field-dwelling creatures. If none of this has them scrambling into their wellies and anoraks, throw in the promise of a bag of crisps and a lemonade at a pub along the way. Once they have left point A with point B in mind (point Bs are important to children. Without a point B there is, literally, no point), children almost always enjoy country walks. But that doesn't mean you won't have to market it hard all over again next time.
Against: There is a small window in a child's life when walking is a fun and novel thing to do. It lasts about six months and comes just after they have learned how to stand, propel themselves forward and trash the house more effectively than when they were simply crawling demolition machines. Very soon thereafter, walking loses its thrill and they will demand to be carried or pushed - anything to avoid making contact with a pavement or, worse, a field, farm-track or footpath. I'd like to say it gets better as they grow up, but the reluctance just takes other forms. Once they have passed the age when they can reasonably be given piggy-backs, hoisted into backpacks or fit into pushchairs, they will whinge, whine and stage sit-down protests in the middle of farmyards. Instead of embracing nature, their worst townie traits come to the fore. They will scream blue murder at the sight of placidly grazing sheep, launch into hysterics at the merest suggestion of mud on their shoes and circle cow pats as if they were unexploded landmines. Not the enriching family stroll you had in mind, then.
Verdict: If you want children to enjoy country walks, avoid inflammatory words like "public footpath", "fresh air" and "exercise". Lean heavily instead on the adventure and the exploring angle. It worked for the Famous Five. Take away the ginger beer and the weird Uncle Quentin and what were they doing but simply messing about outdoors with a dog and some bikes?