The mood that Bryson creates in his book changes quite frequently throughout the course of his book, which is one of the reasons that the book is so entertaining. It shifts from a tone of sarcasm and hilarity, to reverence for the beauty of the woods, to weariness at the monotony of their sameness. Throughout the book, he switches between these moods regularly, mixing them to a nice blend.
Bryson uses a reverent mood and tone to convey how the woods are being negatively impacted by human tramplings and disrespect. He establishes this mood by giving the historical background of the trails and forests, and outlining the impacts of human invasion. He describes their beauty, their tranquility and their solace. Bryson also creates a mood of weariness at the monotony of the woods. As he and Katz walk along, he describes how pretty soon, every tree looks entirely the same, and every sound and leaf all blend into one long and dreary trail. He is sick of trees and wants to see something else--thsi creates a mood of weariness. When Bryson is telling many of his stories, a mood of hilarity is produced. He describes his fear of bears, of the woods and how every noise is amplified and terrifying, and his fearful response--this makes the mood funny and entertaining.
I hope that those thoughts helped a bit; good luck!