Given the Puritans' view of the forest, what atmosphere does Miller create by setting this scene in the woods?
As the first answer states, Miller does not actually set any of his scenes in the forest. The play refers to action that has taken place before the first scene between Rev. Parris and Abigail when Abigail discusses being in the forest. The film version of the play does include two scenes in the forest--the girls' dancing with Tituba and John and Abigail meeting one last time in the forest (this second scene is not part of the play at all).
The Puritans' view of the forest as the devil's earthly home was a common teaching and has often been satirized and portrayed in American Literature. Washington Irving, who regularly mocked Puritan superstitions and traditions, uses the forest as the devil's home in "The Devil and Tom Walker." Nathaniel Hawthorne, relative of the Puritan leader, Judge Hathorne (from The Crucible), sets the "earthy" scenes between Dimmesdale and Hester in the forest for The Scarlet Letter. So, as you can see, the Puritans believed that the darkness of the forest hid the sins or sin nature of mankind from the "light" of God and provided a perfect setting for the devil to roam with his black book looking for humans who were willing to sign away their souls to do the devil's bidding.
The Puritans were a spiritual and superstitious people, a condition they inherited from living in England. In those days, it was typical for people to attempt to explain the unknown with either the scripture (usually references to the Devil) or with the presence of evil spirits.
The woods represent this unknown, this fearful superstition that to stray farther away from the village or the church, or your home for that matter, was to stray figuratively from God as well. Miller does a wonderful job of portraying this common Puritan fear, as well as the sense that the girls have committed a sin by going there at all. It seems an act of rebellion.
I assume that you are talking about the dancing and such that the girls were doing in the woods. We don't actually see it, but it is spoken of.
The Puritans believed (Miller says in his introduction to Act I) that the woods were the last stronghold of Satan himself. Because of this, it would make a great deal of sense to set this scene in the woods. By doing what they are doing in the woods, the girls and Tituba are sort of implying that they are in league with the Devil -- they are conducting their rites in the Devil's place.
So, the atmosphere Miller creates is one of fear, perhaps, and of the presence of evil.