"The old gods stir and will not let me sleep," she heard the woman say. "I dreamt I saw a shadow with a burning heart butchering a golden stag, aye."
This is a vision of the death of Renly (the golden stag) at the hands of the Melisandre's shadow-creature.
"I dreamt of a man without a face, waiting on a bridge that swayed and swung. On his shoulder perched a drowned crow with seaweed hanging from his wings."
The theory proposed for this is that the man without a face is a Faceless Man hired by Euron Greyjoy to kill his brother, Balon Greyjoy. Balon died when falling off a bridge and drowning, and he could very well have been helped along.
"I dreamt of a roaring river and a woman that was a fish. Dead she drifted, with red tears on her cheeks, but when her eyes did open, oh, I woke from terror. All this I dreamt, and more."
The woman who was a fish is Catelyn (the trout being the banner of the Tully's), thrown into the river after she's been killed. The red tears on her cheeks are the blood from where she scratched herself, and her eyes opening herald her resurrection by Beric Dondarrion at the end of A Storm of Swords.