Some materials are strong in response to a slowly applied deformation, yet weak when subject to rapid deformations—a materials property known as strain-rate softening1. Snow exhibits such behaviour: it is comparatively strong at low deformation rates, where it is quasi-plastic, but weak at high rates, where it deforms in a quasi-brittle manner2. During deformation, strain-rate-softening materials ranging from metals3, 4 to micellar systems5 exhibit complex spatio-temporal deformation patterns, including regular or chaotic deformation-rate oscillations and travelling deformation waves6. Here we report a systematic investigation of such phenomena in snow and show that snow can deform with the formation and propagation of localized deformation bands accompanied by oscillations of the driving force. We propose a model that accounts for these observations. Our findings demonstrate that in snow, strain localization can occur even in initially homogeneous samples deforming under homogeneous loads.