Scale-invariant phenomena are common in nature and fractals represent a suitable mathematical tool to describe them. Snow avalanche flow is made up of a mixture of grains and aggregates (granules) which can be broken or sintered together. The granular properties and interactions are important in understanding how avalanches flow. In this paper a fractal model for describing the grain-size distribution in the deposit of a snow avalanche is formulated by introducing the concept of aggregation probability. Although the model is two-dimensional, an extension to the three-dimensional case is proposed in the conclusions. The cumulative size distribution law is extrapolated from the model, and a physical discussion on fractal parameters is conducted. Finally, an experimental application to a real avalanche event is considered to confirm the predictions of the model and to present an extension to multifractality.