Fog can represent a number of different things (estrangement, retreating into one's self, blindness) in Long Day's Journey, but generally, for all of the characters, fog is dark, isolating, and unstoppable. Both Edmund and Mary attempt at various moments to escape or transcend reality, and both use fog as a metaphor or mechanism for doing so.
It's interesting to note that the fog itself isn't enough to generate a mind-altering experience. Edmund experiences his retreat into the fog with the help of alcohol, while Mary relies on morphine. These effects are also by no means limited to Mary and Edmund. James and Jamie may not reference fog explicitly; nonetheless, they both feel as though they've "drowned long ago," and both hide from the world using alcohol. References to alcohol, morphine, and fog all intensify as the play races towards its conclusion.
What, then, of the foghorns and the yacht bells, which periodically cut through the fog? It's Mary who points out that she hates the foghorn: "It won't let you alone. It keeps reminding you, and warning you, and calling you back" (3.1.9). To pursue our analogy of fog and addiction further, the sounds of the harbor act as periodic intrusions of reality into each character's fantasy life. Addiction isn't enough to hold reality at bay forever; there are always the other Tyrones hovering around, ready to chime in and remind each other of their many, many failings.