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Properly initializing land snow conditions with multi-satellite data assimilation (DA) may help tackle the long-standing challenge of Asian monsoon seasonal forecasts. However, to what extent can snow DA help resolve the problem remains largely unexplored. Here we establish, for the first time, that improved springtime snow initializations assimilating the Moderate Spectral Imaging Satellite (MODIS) snow cover fraction and the Gravity Recovery and Climate Experiment (GRACE) terrestrial water storage data can improve the simulation accuracy of Asian monsoon seasonal anomalies. Focusing on the western Tibetan Plateau (TP) and mid- to high-latitude Eurasia (EA), two regions where multi-satellite snow DA is critical, we found that DA influences the monsoon circulation at different months depending on the regional snow-atmosphere coupling strengths. For the pre-monsoon season, accurate initialization of the TP snow is key, and assimilating MODIS data slightly outperforms jointly assimilating MODIS and GRACE data. For the peak-monsoon season, accurate initialization of the EA snow is more important due to its long memory, and assimilating GRACE data brings the most pronounced gains. Among all the Asian monsoon subregions, the most robust improvement is seen over central north India, a likely result of the region's strong sensitivity to thermal forcing. While this study highlights complementary snow observations as promising new sources of the monsoon predictability, it also clarifies complexities in translating DA to useful monsoon forecast skill, which may help bridge the gap between land DA and dynamical climate forecasting studies.