If your kart has 4" ground clearance and treaded tires it's good for trail riding if you have trails that are appropriate for that kind of thing. I did allot of that in my younger days. Just watch out, sometimes a tree will jump out in front of you and get ready to weld frame cracks on occasion.
Many of our cities and towns now have what's called the Guns Down Wheels Up Rollout where you can ride on any city street or sidewalk anytime you want with dirt bikes and quad runners dodging cars, people ect. Check with your local democratic officials for details.