Hi JohnBrainard,
I don't think overcast days should prevent you from going out and taking some good photographs, especially if you can capture things such as broody clouds, heavy rainfall, and stormy coloured tones. For instance, here's a photo I took on the beach when it was really quite dull and cloudy. OK, so it's not the best photo, there are plenty of ways to improve it, but I am simply using it as an example:
Get out there, take some good bad-weather photos. Let's see what you can do!