Understanding the dynamics driving the transformation of snowfall crystals into blowing snow particles is critical to correctly account for the energy and mass balances in polar and alpine regions. Here we propose a fragmentation theory of fractal snow crystals that explicitly links the size distribution of blowing snow particles to that of falling snow crystals. We use discrete element modeling of the fragmentation process to support the assumptions made in our theory. By combining this fragmentation model with a statistical mechanics model of blowing snow, we are able to reproduce the characteristic features of blowing snow size distributions measured in the field and in a wind tunnel. In particular, both model and measurements show the emergence of a self-similar scaling for large particle sizes and a systematic deviation from this scaling for small particle sizes.