We propose a three-stage stochastic programming model to inform risk-averse investment in power system resilience to winter storms. The first stage pertains to long-term investment in generator winterization and mobile battery energy storage system (MBESS) resources, the second stage to MBESS deployment prior to an imminent storm, and the third stage to operational response. Serving as a forecast update, an imminent winter storm’s severity is assumed to be known at the time the deployment decisions are made. We incorporate conditional value-at-risk (CVaR) as the risk measure in the objective function to target loss, represented in our model by unserved energy, experienced during high-impact, low-frequency events. We apply the model to a Texas-focused case study based on the ACTIVS 2000-bus synthetic grid with winter storm scenarios generated using historical Winter Storm Uri data. Results demonstrate how the optimal investments are affected by parameters like cost and risk aversion, and also how effectively using CVaR as a risk measure mitigates the outcomes in the tail of the loss distribution over the winter storm impact uncertainty.