Talking of Frodo's dreams, there is also the rather disturbing poem in The
Adventures of Tom Bombadil called The Sea Bell, with the subtitle 'Frodo's
Dreme'. This was supposedly related to the dark despairing dreams Frodo
had on his return to the Shire, and I think shows how psychologicaly wounded he
was.
Dreams generally are quite important in Middle-earth, if you are interested
there is a rather academic book that explores them by Verlyn Flieger, called
"A Question of Time: J. R. R. Tolkien's Road to Faėrie" There is a review
of it on the Tolkien Society Web
page.