Browsing the web without a goal feels to me more like daydreaming than it feels like walking in the woods.
Sometimes I daydream while walking in the woods, but I am more likely to daydream while staring at a blank wall or while waiting for a bus on a boring street with nothing but concrete and asphalt rectangles to look at.
In fact, my whole purpose in walking in the woods is to stop the mental chatter, including the daydreaming. If I find myself daydreaming during the walk, I consider that a failure and tell myself that next time I walk in the woods, I should take along a friend or a dog to make the walk more engaging and consequently more effective at stopping the chatter -- or that I should find more interesting woods.
This comment could be extended greatly by introducing the concepts of "focused attention" and "involuntary attention". Very briefly, focused attention is how we pay the bills and contribute to advancing our civilization and all, but focused attention eventually tires the mind. The best way to recover from the tiredness and to restore the ability to focus the attention is to do things that engage "involuntary attention", e.g., taking a walk in the woods where there are things that attract attention involuntarily (without raising the blood pressure like the sirens and the horns of the city tend to do). That will restore the ability to pay focused attention (to whatever the person choose to focus on) faster than would being in a room alone and staring at a blank wall. Some people advise spending as much time as possible either engaging in focused attention or recovering the ability to focus one's attention and advise against daydreaming and aimless browsing of the web because those are sub-optimal ways of restoring the ability to focus attention. (Spending time with friends or walking in the woods with a dog are much better ways.)