Stratospheric Sudden Warmings (SSWs) significantly affect surface climate in boreal winter. However, their impacts vary considerably from one event to another: more than one-third of SSWs are not followed by expected tropospheric anomalies. To isolate the forced responses to SSWs, this study analyzes model experiments from the Stratospheric Nudging And Predictable Surface Impacts (SNAPSI) project, where the stratospheric zonal-mean state is nudged using either observations or climatology. The differences between the two experiments are examined within a multi-model ensemble framework. Nudging experiments conducted for the 2018 SSW, which featured significant tropospheric responses, and the 2019 SSW, which showed none, reveal that both SSWs consistently drive a negative Northern Annular Mode over time. The forced tropospheric response is primarily driven by an increase in Arctic surface pressure resulting from poleward mass fluxes in the stratosphere and upper troposphere. The poleward mass fluxes are initially induced by the zonal wind nudging in the middle stratosphere and subsequently by the eddy heat and momentum fluxes in the stratosphere and upper troposphere. This result suggests that while SSWs intrinsically drive tropospheric anomalies, the internal variability in the troposphere strengthens or suppresses the forced anomalies from the stratosphere, which may determine the existence of expected tropospheric anomalies following SSWs.