Emphasizing Depth

As objects become progressively further from your camera, not only do they become smaller, but they also lose contrast -- and sometimes quite dramatically. This can be both a blessing and a curse, because while it exaggerates the difference between near and far objects, it also makes distant objects difficult to photograph in isolation.
In the example to the left, there are at least four layers of trees which cascade back towards the distant bridge. Notice how both color saturation and contrast drop dramatically with each successively distant tree layer. The furthest layer, near the bridge, is reduced to nothing more than a silhouette, whereas the closest layer has near full color and contrast.

Although there are no steadfast rules with photographing in the fog, it's often helpful to have at least some of your subject close to the camera. This way a portion of your image can contain high contrast and color, while also hinting at what everything else would look like otherwise. This also serves to add some tonal diversity to the scene.