Natural threats can affect electricity system infrastructure, leading to multiple, dependent contingencies and extensive load outages. Given the high costs of such load interruptions, transmission system operators (TSOs) are interested in predicting potentially critical scenarios and applying appropriate preventive and/or corrective countermeasures. Pollution is a non-negligible environmental cause of component failures, because it causes flashover of insulators with different mechanisms. In order to increase the resilience of the electricity system to these events, one fundamental step is to analyze the vulnerability of insulators to polluting deposits. The article presents a model for quantifying the vulnerability of insulators to two main flashover mechanisms, caused by pollutant deposits in humid conditions and by the build-up of snow in the presence of sea salt. The model is integrated within a resilience assessment tool and can be used in different application contexts (from long-term studies to support for exercise programming). The application of the tool to a realistic case study, referring to a portion of the Italian AAT/AT network, demonstrates the effectiveness of the vulnerability model both in calculating the return to failure times of components due to pollution and in anticipating critical situations in the electricity system.