Does increased solar activity lead to mild winters?

The link between solar activity levels and the weather on earth is still under debate. However, it is though that during periods of increased solar activity, fewer cosmic rays are able to reach the earth. This is believed to have an impact on cloud and temperature levels. We believe the weather in England during these periods tends to be milder and wetter than would have been the case with lower levels of solar activity. However, this is only one of many factors, and cold winters have been recorded in both periods of high solar activity and low solar activity.