Snow cover variation significantly impacts alpine vegetation dynamics on the Tibetan Plateau (TP), yet this effect under climate change remains underexplored. This study uses a survival analysis model to assess the influence of snow on vegetation green-up dynamics, while controlling for key temperature and water availability factors. This analysis integrates multi-source data, including satellite-derived vegetation green-up dates (GUDs), snow depth, accumulated growing degree days (AGDD), downward shortwave radiation (SRAD), precipitation, and soil moisture. Our survival analysis model effectively simulated GUD on the TP, achieving an R of 0.62 (p < 0.01), a root mean square error (RMSE) of 11.20 days, and a bias of -1.41 days for 2020 GUD predictions. It outperformed both the model excluding snow depth and a linear regression model. By isolating snow's impact, we found it exerts a stronger influence on vegetation GUD than precipitation in snow-covered areas of the TP. Furthermore, snow depth effects varied seasonally: a 1-cm increase in preseason snow depth reduced green-up rates by 8.48% before 156(th) day but increased them by 4.74% afterward. This indicates that deeper preseason snow cover delays GUD before June, but advances it from June onward, rather than having a uniform effect. These findings highlight the critical role of snow and underscore the need to incorporate its distinct effects into vegetation phenology models in alpine regions.