Dry slab avalanches release by propagation of shear fractures in a thin, planar weak layer underneath a cohesive, stronger slab. This implies that a balance between shear fracture toughness and the shear fracture stress intensity factor fundamentally determines snow slab stability. Conventionally, fracture toughness is a material property and, for most materials, emphasis is on tensile fracture since most materials fail first in tension. However, for the snow slab, the weak layer fractures first, and field measurements show that the slab material is always stronger than the weak layer. Snow slabs in nature vary with respect to mechanical properties and other characteristics, so the concept of fracture toughness as a material property has no relevance when it is calculated for different avalanches. In this paper, field measurements collected from hundreds of snow slabs are combined with the cohesive crack model to yield estimates for the mode II shear fracture toughness, KIIc. The results suggest that the snow slab has extremely low fracture toughness with variations in nature over more than two orders of magnitude. The nominal weak layer shear strength τNu has a power law relationship with respect to the fundamental scaling parameter: the slab thickness, D. Model results also imply that KIIc has power law scaling with respect to D. It is also shown that KIIc follows a log-normal probability density function. This implies a multifractal character by considering the moments, q, of shear fracture toughness scaled with D. Positive multifractal dimensions are suggested for q up to approximately 2.