In this work we develop a machine learning based model for computing a probabilistic prediction of the number of distribution grid customers that will lose power during a given severe weather event. The model takes as input a prediction of damage counts at the level of substation regions or service regions, as proposed in earlier work, and generates the customer count impact forecast in aggregate for the entire service territory (or a large region thereof). The relationship between damage count and customer count is highly noisy in general, given the branching structure of distribution grids. Here we exploit the fact that the noise reduces as the damage count increases and develop a Tobit model applicable for severe weather events. We validate the forecasting system using data from a utility.