Compression of snow at low strain rates governs the natural densification of snow and firn on Earth. Different deformation mechanisms (e.g., grain boundary sliding and dislocation creep) are widely employed in models and are mainly believed to change depending on relative density or snow type. To explore this picture, we conducted compression experiments with a nominally constant strain rate ɛ̇ ≈ 10^-6 s^-1 and systematically varied snow type, density, and specific surface area. We used a micro-compression stage to enable X-ray micro-tomography imaging and microstructure characterization before and after the experiment. Using repeated load-relaxation cycles, we eliminate changes in the microstructure that occur during the first loading, allowing us to probe the viscoplastic behavior of the intact ice matrix. To evaluate the effective mechanical behavior of snow, we derived an implicit, analytical solution of a non-linear scalar model that characterizes loading and relaxation in terms of the stress exponent n in Glen's law. Our results evidence a sharp transition of n as a function of the geometrical grain size, and rule out that this transition is caused by density or snow type. The derived values of n ≈ 1.9 for small grains to n≈4.4 for large grains are consistent with a transition from grain boundary sliding to dislocation creep at a transition grain size of around 0.5-0.6 mm. Our results shed new light on the old discussion about deformation mechanisms in snow and firn.