I rewatched Mulholland Drive recently and discovered that the woman who plays the guy in the diners nightmare and appears from behind a wall is Bonnie Aarons an actress previously told she'd never make it in Hollywood on account of her looks. It seemed important that Lynch had specifically chosen that actress for the role. The nightmare she signified was failure, the fear of failure in Hollywood. 

Feels equally important that he chose an Abraham Lincoln lookalike to play the Woodsman. His appearance is kind of similar to the Mulholland drive character, although he's covered in soot and blacked up in appearance. If Abraham Lincoln signified some kind of hope and the abolition of slavery, this 'bad' Abe certainly came back to in 1956 to wreak havoc, heading towards a radio station that would be broadcasting music at the dawn of rock n roll to broadcast his own biblical message mixing up metaphors of horses, water and wells.

I think the phrase he repeats is basically saying here is good, the pure, if you deplete that resource you'll descend into darkness. The horse, a white horse can symbolise the balance of power and wisdom, the white of the eyes signifies danger and your fears of death and darkness of evil.

The message he repeats sends everyone asleep and seems to awaken the egg/s hatching to find their hosts. As they sleep, in their subconscious states their fears enter them quite literally in the case of the girl.