Accurate electricity demand prediction is an essential task for supporting power balance, energy trading, and demand-side management in power systems. Extreme weather events, such as winter cold spells or summer heatwaves, can result in unprecedented peak demands due to sudden heating or cooling needs. In those cases, the point demand prediction presenting a single possibility is not sufficient. The system needs to adopt the probabilistic forecast which produces the whole load probability distribution to assess diverse grid scenarios and future uncertainty. This work examines the impact of weather information on machine-learning probabilistic electricity demand predictions. The case study is performed on six European countries involving a great diversity of weather conditions, heating, and cooling needs.