Climate change and its impact on everyday life still remains one of the greatest challenge of our era. The complex nature of climate data addresses the use of data science techniques to provide predictive analytics to the task at hand. While most existing approaches exploit correlation between observations and features to improve forecasting, the present work deals with causality, a principle that enhances robustness and provides better insight to domain experts. More specifically, a novel framework for causality discovery is proposed, based on statistical (i.e. Granger causality tests) as well as on non-linear state space reconstruction algorithms (i.e. Convergent Cross Mapping, a very effective algorithm in dynamic systems, such as the task at hand) in order to find the causal relations between meteorological time series. Furthermore, the framework also supports methods for graph analysis, thus providing informative visualizations on the influential levels of causality. Experiment results on a dataset of real observations from different cities of Greece, obtained through crawling of Internet sites of Davis weather stations demonstrate the ability to model and visualize the relations of the meteorological parameters amongst the cities. Moreover, by utilizing such causal inference knowledge, the forecasting performance for each city is significantly improved, since only relevant and informative features were taken into consideration