Accurate mountainous snow estimation is paramount for hydrological processes and water resources estimation in arid regions. Using Land surface models (LSMs) is a practical numerical approach for snow estimation in a complex orography region such as the Tianshan Mountains. However, the bias of precipitation forcing is a major source of uncertainty for snow simulation over scarce-data regions. This study evaluated the performance of 4 km snow simulations using the Noah-MP LSM driven by eight precipitation sources. They are retrieved from non-model products and climate model simulations during the 2018-2019 cold season in the Central Tianshan Mountains (CTS) region. Multi-source validation datasets (in-situ observation, field snow pits, and remote sensing products) have been used for evaluation and uncertainty estimation. The results showed that the difference in precipitation amount significantly affected the snowpack simulation performance. Compared with non-model products (Global Land Data Assimilation System (GLDAS), Global Precipitation Measurement (GPM), and Gauge-adjusted Global Satellite Mapping of Precipitation (GSMaP)), the cold season precipitation from climate model simulations exhibited a better performance overall in the high-elevation regions (elevation > 1000 m) evaluated by in-situ observations. In addition, the 4 km convection-permitting modeling (CPM) precipitation (WRF-Morrison and WRF-WSM6) showed higher accuracy (RMSE: 23.48 mm/season and 18.94 mm/season, respectively) than gray-zone resolution simulations and ERA5-land driven runs in the high-elevation regions. The snow depth simulation driven by WRF-Morrison precipitation had the second smallest RMSE (4.67 cm/day) and lowest bias (-0.74 cm/day) value in the high-elevation regions compared with in-situ observation. Meanwhile, CPM precipitation-driven runs exhibited the smallest RMSE value based on the assessment of snow field pits. In addition, the CPM-driven simulation achieved the closest match to the elevation-based distribution of snow cover days in regions with elevation over 1000 m and duration over 60 days compared to the MODIS product. The findings of this study highlight that CPM with proper parameterization configurations has added values in producing realistic topographic precipitation for snow modeling using LSMs over data-scarcity mountainous areas.