Understanding the complex interactions between rubber and snow is vital for enhancing tire traction in winter conditions; such interactions include the process that occurs during contact between the tire tread and snow, particularly during sliding. Recognizing the inherent complexities of these interactions, especially under varying applied loading rates, a dual methodology is used: detailed computational simulations and experimental validation. To capture the diverse behaviors exhibited by snow, an advanced elastoplastic constitutive model at finite strains is used. This model is enriched by an implicit gradient damage enhancement to replicate the brittle nature of snow under high loading rates. After calibration against established experimental benchmarks, the proposed material model is shown to demonstrate a suitable alignment with observed behaviors. Further computational simulations provide insights into different examples of the rubber–snow interaction, whereas experimental data are used to validate our approach. This affirms the potential of the proposed framework as a robust tool for modeling the intricate interaction between rubber and snow.