The full-hydrometeor four-dimensional variational (4D-Var) assimilation scheme in the Weather Research and Forecasting (WRF) model, based on the WRF single-moment 6-class microphysics scheme (WSM6), is utilized to assimilate precipitation data. The focus is on short-term convective precipitation forecasts influenced by the Northeast cold vortex (NCCV). Four assimilation experiments were designed to compare the warm rain scheme with the full-hydrometeor scheme, as well as to examine the differences between assimilating hourly surface rain gauge data and multi-source integrated precipitation products. Ten cases of intense convective precipitation related to NCCV were analyzed. The results demonstrate that the initial analysis of ice-phase hydrometeors was satisfactory across the three experiments utilizing the full-hydrometeor 4D-Var schemes. The assimilation of precipitation data full-hydrometeor scheme in WRF 4D-Var effectively adjusted atmospheric thermodynamic properties and decreased model spin-up time, leading to improved precipitation forecasts, especially for the 0-3 hour period. Furthermore, the assimilation of rain gauge data or multi-source integrated precipitation data has been demonstrated to be an effective approach for enhancing the accuracy of weather forecasts.