I go on walks with no destination all the time. In fact, I rarely do the sort of hiking that Dr. D attributes to the male gender except when invited to do so by a female friend. I think his statement says more about him and his ideology than it says about gender differences, real or perceived.
I hunt. Unless a hunter uses a high-powered rifle that allows the targeting of distant animals, hunting requires the hunter be in wandering mode, with all senses and focus relaxed. If we're focused and thinking, the electromagnetic fields we emit are out of phase with our landscape and we stick out like a sore thumb, no matter how well camouflaged our clothing is. If we quiet our thinking mind, our electromagnetic fields can synch with those of a landscape and we blend in, even if our clothing stands out.