He has dreams in which he sees himself walking alone. The dreams don't give him (his mind, not body) the proper rest that sleep is actual meant for. Seeing himself alone like that, even if it's only dreams, makes him restless. Therefore, the mood is very sad, as the singer feels lonely. The other sentence is about how he uses his collar of his jacket as a physical shield against the cold and wet weather, which may be a metaphor for the feeling his surroundings give him.

"I turn my collar to the cold and damp" - means that he is turning up his collar around his neck to warm and shield himself from the cold and wet (damp) weather. The cold and damp weather is a symbol for his feelings of loneliness and desolation.