Is there less precipitation (rain/snow) in cold weather than in warm weather? To me it seems that there is a lot less precipitation when temperatures go below -5°C (23°F).

Is there any evidence for that? Could this be a local phenomenon (I live in Germany)? What could be the cause for this?

I tried searching for charts that show precipitation over temperature, but all I could find were charts that showed precipitation over months of year which is not quite the same.
In most of Western Europe, precipitation comes from westerly winds formed over the warm waters of the Gulf Stream current that flows from the Caribbean to Western Europe. That is a warm current, so these winds would be warmer and make your area warmer. Besides, as they come from a warm ocean they are moist and carry water vapor and make clouds. Low temperatures are usually caused by easterly/northerly winds originating in Siberia, these are cold and come from land. Cold winds cannot carry moisture and on top of that they travel over land rather than the ocean and are dry. So in most cases in European winter, relative warmth and precipitation go hand-in-hand.