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Electrical power transmission networks of many developed countries are undergoing deep transformations aimed at (i) facing the challenge offered by the stochastically fluctuating power contributions due to the continuously growing connections of renewable power generating units and (ii) decreasing their vulnerability to failures or malicious attacks and improving their resilience, in order to provide more reliable services, thus increasing both safety and profits. In this complex context, one of the major concerns is that related to the potentially catastrophic consequences of cascading failures triggered by rare and difficult to predict extreme weather events. In this work, we originally propose to combine an extreme weather stochastic model of literature to a realistic cascading failure simulator based on a direct current (DC) power flow approximation and a proportional re-dispatch strategy. The description of the dynamics of the network is completed by the introduction of a novel restoration model accounting for the operating conditions that a repair crew may encounter during an extreme weather event. The resulting model is solved by a customized sequential Monte Carlo scheme in order to quantify the impact of extreme weather events on the reliability/availability performances of the power grid. The approach is demonstrated with reference to the test case of the IEEE14 power transmission network