I am re-reading Tolkien's The Hobbit (in anticipation of the movie), and was wondering if there was some further significance to the appearance of the white stag/deer. In the chapter "Flies and Spiders" after the dwarves and Bilbo ford the enchanted stream they hear horns of a hunt and the deer appear; the dwarves shoot at them, missing completely. This would lead me to believe that the deer were phantoms, or at least enchanted. Tolkien then writes that:
if they had known more about it and considered the meaning of the hunt and the white deer that had appeared on their path, they would have know they were drawing towards the eastern edge
Other than the fact that the deer are white, which are traditionally considered magical (eg Narnia, Native American tales), is there another reason that the hunt and the deer should be a signal of the end of the forest? Is there a piece of Tolkien lore I am missing?