Snow avalanche-induced air-blasts are capable of breaking trees, damaging buildings and causing fatalities. Predicting their destructive properties is an essential part of snow avalanche hazard mitigation. Here, we propose a depth-averaged model that involves turbulent fluctuations to simulate the air-blast dynamics. The turbulent energy of the air-blast arises from that of dust-mixed air transferred from the avalanche core, shearing work in the cloud and entrained air, and is exploited to improve the air entrainment and drag relationships. We further present a unique data set of air blast-induced tree breakage, providing type, status, diameter and falling direction of the measured trees. Through case studies of two artificially released avalanches with measured powder heights and three natural avalanches with tree-breakage information, we test the model and investigate the turbulence effect on air-blast dynamics. The proposed model and tree-breakage data set quantify the air-blast destructiveness and can be applied for avalanche hazard assessment.