I don't recommend using a white balance tool in this case. That would result in altering the gray fog to the correct color, but it will also bring out the blue in the sky, which you don't want. So I'm going to suggest using a levels tool. Many applications have this and it's really easy to use once you know how. In this example I used Pixlr, which is free and can be run within Google's Chrome browser as an app, installed from their webstore, but Adobe's Photoshop and Apple's Aperture both have a levels tool too.

Here is a levels tool from Photoshop as an example (they all look similar):
(source: computer-darkroom.com)

The levels tool shows you a histogram of the color distribution (left is darkest, right is brightest) organized by color channel and some sliders. You will also be able to choose the color channel if you want to adjust just one: RGB, Red, Green, or Blue. In this case leave it on RGB. As standard practice in the histogram, move the arrow/tab for the input sliders to the left (dark) and right (light) to the extents of the histogram (or in further if you want to clip some colors off). This will help the image fill the entire used tonal range and prevent a washed out effect.

Once you've done that, your image should look a lot better, as the gray tones of the fog are more neutral. You can now enhance the hazy effect of the fog by clipping the right most slider further in - this removes the light tones as much as you want. If you adjust the middle slider, this will create a brightness/contrast effect that applies to almost the entire image - it could be useful, but I left it alone. Here's my before/after with about 1 minute of adjusting the levels:

Before: After:

You can probably achieve exactly what you're looking for with a bit more time and effort (the blue vignette in the top left is annoying me), but the levels tool is where you should start. If you start to see blues that you don't like, then change the channel to Blue and move the left most slider in and adjust the output level as well. From there you can play with hue and saturation to keep things looking balanced. Ultimately though, play around and get familiar with the levels tool. It's invaluable!