In mountain territories, snow avalanches are a prevalent threat. Long-term risk management involves defining meaningful compromises between protection and overall sustainability of communities and their environment. Methods able to (i) consider all sources of losses, (ii) account for the high uncertainty levels that affect all components of the risk and (iii) cope for marked non-stationarities should be employed. Yet, on the basis of a literature review and an analysis of relations to Sustainable Development Goals (SDGs), it is established that snow avalanche risk assessment and mitigation remain dominated by approaches that can be summed up as deterministic, hazard oriented, stationary and not holistic enough. A more comprehensive paradigm relying on formal statistical modelling is then proposed and first ideas to put it to work are formulated. Application to different mountain environments and broader risk problems is discussed.