Snow exhibits complex mechanical behavior characterized by time-dependent, rate-sensitive responses that encompass viscoelasticity, plasticity, and damage evolution. This study presents an integrated numerical framework that unifies two advanced modeling approaches — an elasto-visco-plastic-damage model and a visco-elasto-plastic-damage model — to capture the different responses of snow under varying loading conditions. Building upon established elasto-plastic-damage formulations [1], the framework extends the constitutive description to incorporate both viscoelastic and viscoplastic effects, thereby addressing the influence of different strain rates on snow deformation and failure. The models are implemented within a Finite Element (FE) framework and calibrated using experimental data from the literature. Results demonstrate that the proposed models effectively capture the interplay between time-dependent behavior, plastic yielding, and progressive damage, offering enhanced predictive capabilities for snow behavior at different loading scenarios. These insights are critical for improving the design and analysis of structures interacting with snow and contribute to a deeper understanding of snow mechanics in engineering applications.