Another alternative to a cart would be a wagon (a la Radio Flyer). You may have to find a larger one if you have more than one child, and you may have to fashion a restraint system (to strap in a car seat or something). But, they may work well as they can hold additional cargo and they work over varying terrain.

If anyone has any other pros or cons to this, pipe up, because this is purely my imagination. I have no kids and no wagon, so no experience with either.