On page 179 of Nathaniel Hawthorne's The Scarlet Letter, Hester sends Pearl off to play in a different area of the forest as she, Hester, observes Mr. Dimmesdale. In this scene, as in the rest of the novel, the forest serves as an extension of the characters minds, as a safe haven from the surrounding world. Through Pearl's separation from the brook, Hester's shooing of Pearl, and Dimmesdale's hopeless appearance, the forest gives deeper details into the characters in The Scarlet Letter.

I like the phrase "extension of the characters minds". I'm interested to see what you have to say about each of those 3 ideas in your thesis.
A good start, Patrick. The setting is often a way an author communicates a deeper understanding of the characters. Is there evidence from the book to support the opposing claim, "No, the forest does not give deeper details into the characters"? Probably not. But you might find two different messages the forest might give -- maybe one is hopeful, the other is threatening? Is the forest always a safe haven? Is it equally "safe" to all the characters? Does the forest play the same role in all parts of the book? Your paper needn't answer all those questions, of course -- those are just some things to think about as you look for the evidence pro and con.