In the northern hemisphere, snow accumulating on trees and overhead lines causes widespread outages in the electricity distribution networks. Accurate outage risk models are an essential element in improving the resilience of modern distribution networks. In this paper, a Random Forest-based model for estimating the susceptibility of overhead lines to outages caused by tree crown snow loads is proposed. The model uses a novel combination of an aerial inspection outage risk dataset, an advanced forest crown snow load risk map, a canopy height model, and forest characteristics data. All predictor variables used in the study are available as open data. As a result, outage risk probability in 50 m overhead line sections for a distribution network was generated. Cross-validation of the model showed a good predictive performance with a receiver operating characteristic area under curve (ROC AUC) of 0.75 and an accuracy of 0.74. The impact of the predictor variables was investigated by using Shapley additive explanations (SHAP) values. The most impactful variables were the forest crown snow load risk, the number of nearby canopy height model pixels, and the birch tree volume. The outage risk probability model developed in this paper could be similarly applied to assess the crown snow load risk in other distribution networks or even in other types of networks, such as roads and railways.