We present simple scaling relationships that allow us to predict the main dynamical characteristics (height, length and velocity) of constant-volume snow avalanches with minimal input data. In particular, we show that both avalanche height and length can be expressed as a function of the avalanche volume and the distance travelled by the front, independent of the specific rheological parameters of the snow. These scaling relationships are derived from a large-time asymptotic solution to the avalanche dynamic equations, corresponding to a balance between gravity and Voellmy friction (the kinematic wave approximation). Numerical simulations of the complete hydraulic shallow-flow equations confirm that this asymptotic solution, and the predicted scaling relationships, capture the main avalanche characteristics, even for relatively small travel distances. Though derived under restrictive assumptions, we argue that the scaling relationships described in this paper may constitute useful tools for avalanche engineering and design of protective structures.