Cooler weather comes with more cloudy days. The second half of October through November and December is a particularly cloudy time of year. Sometimes, when you look up at the clouds, you see cloud details. However, sometimes the clouds in the sky appear featureless; just a plain, dull gray. When you look up at a cloudy sky and cannot see any features at all, you are usually looking at virga. This is rain or snow, and usually snow, falling from the cloud into dry air and then turning back into cloud material. This reformed cloud has no structure and so looks like a lot of gray nothing.
Cold air is often dry, so it is quite common for light precipitation in the cold months to turn into virga. Doppler radar will often show this as light rain or snow because the Doppler beam is passing through at cloud level instead of down at the ground. From the ground, we just see gray.