The most common comment I hear from students during my fall foliage workshops is how their photos rarely capture the saturated colors they saw when taking their photos. This is usually the result of one of two factors: shooting in mediocre mid-day light that adds blue cast to their photos, and/or not using a polarizer when shooting under diffuse overcast light. A polarizing filter is a must have in any nature photographer's bag. It's traditional use of darkening and adding contrast to blue skies is the least important reason to have a polarizer in my opinion. However, when you duck into the woods for some forest or waterfall photography, this simple filter can make the difference between a mediocre photo and one that instantly captures the viewers attention. I almost always try a polarizer on scenes like the above maple and stream shot in Acadia National Park. There's no blue sky to be found, but the polarizer reduced the reflections coming off of the waxy surface of the leaves, thus showing more of the lush orange of the maple leaves. It also reduced glare on those calmer parts of the stream, turning them from a muddled gray to a richer black, adding pop to the photo by creating contrast between the white water and the calm water.
I shot the above three photos yesterday to illustrate the difference of shooting a water and forest scene with different filters. All three were shot with the same F-stop and processed with the same develop settings in Lightroom. The shutter speeds were 1/5 second for the first photo. 0.8 second for the second photo, and 15 seconds for the 3rd photo. The first two photos show the effect of using a polarizer. In this scene, the color of the foliage doesn't vary much, but the polarized shot shows more contrast in the water, which I tend to like better. For the 3rd shot, I used a variable neutral density filter to reduce the amount of light reaching the camera's sensor so I could use a long exposure and blur the water even more than in the polarized shot. Which is better is subjective obviously, but I really like the longer exposure in this case.