Years ago I was visiting an uncle on the east coast. One morning it was very foggy and I grabbed my camera and tripod and headed out the door to make some images. As I passed a someone on the street they said to me “it’s not a very good day to take photographs!” My response was too say “No its a great day to make photographs”

My point here is that when you have weather rather than sunshine do not think that you should not be making images. The attached image was made early one foggy morning, and it is the fog that really makes this image stand out.
So as long as you keep your equipment dry and clean get out and make images, You find the results very pleasing.