The reason you are having difficulty finding naturalism in Hawthorne's novel is because it is not there. Naturalism came later than Hawthorne's 1850 novel. Writers associated with naturalism include Stephen Crane (The Open Boat, 1897) and Jack London (Call of the Wild, 1903), for example.
"The application of principles of scientific determinism to fiction and drama and makes the assumption that everything that is real exists in nature, which is defined as the world of objects, actions, and forces possessing significance revealed only through scientific inquiry."
While there is a good deal of NATURE in The Scarlet Letter, naturalism, as a literary principle, does not exist.