Impacts of sudden stratospheric warming (SSW) on three severe cold events (C1–C3) over Northern Hemisphere in early 2021 were investigated using subseasonal‐to‐seasonal ensemble forecasts. The SSW was characterized by successive displacement and split of the stratospheric polar vortex (SPV). Ensemble‐based sensitivity analyses showed that C1 over Siberia and C2 over western Canada were more related to SPV variations at a lead time of 1–2 weeks than C3 over central U.S. Within ensemble forecasts, a more elongated SPV with higher geopotential height over northern Eurasia were conducive to C1, whereas a SPV with the more poleward retreat from displacement contributed to C2. The forecast accuracy of stratospheric heights over the sensitive region at 2 weeks lead was significantly correlated with the forecast skill of the tropospheric circulation pattern preceding C1, implying that prediction of specific cold weather events may be improved by a better forecast of key features in SPV variations. Plain Language Summary: Unusually extreme cold events have frequently occurred during the boreal winter in recent decades. These cold air outbreaks at the surface can be profoundly influenced by variations in the stratospheric polar vortex (SPV) with a lead time of weeks. The winter of early 2021 was characterized by successive extreme cold events over Asia and North America, leading to huge societal impacts, such as the unprecedented power outages over central U.S. in mid‐February 2021. These cold events were accompanied by a weak SPV that had been successively displaced and then split. Based on real‐time ensemble forecasts, we show that weakening and stretching of the SPV contributed to the cold event over Siberia. By contrast, the return of the SPV from displacement favored the cold event over western Canada. The subsequent cold surge over central U.S. was more related to mid‐latitude tropospheric processes than stratospheric processes. The prediction of some extremely cold weather events may be significantly improved by more accurate forecasts of the key features of the evolution of the SPV with a lead time of about two weeks. Key Points: Sudden stratospheric warming with a displaced‐to‐split polar vortex in early 2021 had significant influences on surface cold eventsCold event in Siberia (Canada) was related to weakening (poleward retreat between displacement and split) of stratospheric polar vortexAccurate forecasts of stratospheric variations improved forecast of the tropospheric pattern preceding the cold event over Siberia [ABSTRACT FROM AUTHOR]