The literature disagrees about the statistical distribution of snow avalanche crown depths. Large datasets from Mammoth Mountain, California and the Westwide Avalanche Network show that the three-parameter generalized extreme value distribution provides the most robust fit, followed by a two-parameter variation, the Fréchet distribution. The most parsimonious explanation is neither self-organized criticality nor other complex cascades, but the maximum domain of attraction, implying that distributions of individual avalanche crown depths are scaling. We also show that crown depths do not have a universal tail index. Rather, they range from 2.8 to 4.6 over different avalanche paths, consistent with other geophysical phenomena such as wildfires, which show similar variability.