It’s not always bad weather, … it is unusual weather.
Even though there may be bad in inclimate weather, it doesn’t mean good, or even great photographs cannot be created.
The cloudy or foggy weather can isolate colors or giving a color image a monochrome look.
1.Bracket your exposures, Sometimes the even exposure is not the most interesting. Over or under exposed can add some drama or feelings to the photograph.
2. Try a telephoto lens. A telephoto compresses the scene, bring the foreground, mid-ground, and background closer together and can magnify an effect such as FOG.
3. “Rain also has some unique photographic advantages: it saturates colors, puts a glossy surface on subjects like leaves and grass and, at night, drips colorful reflections across rain-soaked streets.” (http://www.jeffwignall.com/tutorials/weatherphotography.html)
4. PROTECT your camera if there is rain, wind, fog, anything wet around, or where dust particles can blow. Keep in a bad when not shooting, wrap with saran wrap, use umbrellas, or keep in a plastic bag and punch a whole for the lens.
5. Try different white balance settings. It can really effect the colors. And even a cloud or shade white balance can warm things up.
6. Look 360 degrees. Watch how lighting, clouds, puddles, or even foliage and people can look, and look different in a few minutes. Watch for reflections in water, rain drops, windows and mirrors. Or even try shooting thru windows.
7. Wind can be an enemy with flying dirt and dust, let along cold. But remember to keep an close on on them. Photographing wind, or showing something blowing adds a strong feeling to the image.
8. Don’t forget the tripod. It might be necessary with the low light, or be a tool to show things blowing.