Sweet Dreams

[Neithan]

As far as I know there has not yet been a thread on dreams in Tokiens works (at least I couldn't find any) so here goes.
Tolkien uses many dreams for effect in LotR the first example that comes to mind is in the House of Tom Bombadil, Merry and Pippin were given nightmares by the "nightly noises" of the Forest. Frodo, on the other hand, had a dream that told of things that were actually happening to Gandalf. Sam slept on without any dreams at all. What is Tolkien saying about the differences in the characters?
The next night Frodo dreams the exact vision he has when sailing to the west.

Another dream that I thought of was the night before Frodo entered the Old Forest.

Eventually he fell into a vague dream in which he seemed to be looking out of a high window over a dark sea of tangled trees. Down below among the roots there was the sound of creatures crawling and snuffling. He felt sure they would smell him out sooner or later.
Then he heard a noise in the distance. At first he thought it was a great wind coming over the leaves of the forest. Then he knew that it was not leaves, but the sound of the Sea far-off; a sound he had never heard in waking life, though it had often troubled his dreams. Suddenly he found he was out in the open. There were no trees after all. He was on a dark heath, and there was a strange salt smell in the air. Looking up he saw before him a white tower, standing alone on a high ridge. A great desire came over him to climb the tower and see the Sea. He started to struggle up the ridge towards the tower: but suddenly a light came in the sky, and there was a noise of thunder.

Any ideas what this means?

Here is one from The Hobbit,

But all night he dreamed of his own house and wandered in his sleep into all his different rooms looking for something that he could not find nor remember what it looked like.

I like this but I don't know why. I can't figure out what it means, any ideas?

Feel free to bring up any other dreams to discuss as well.