Sudden stratospheric warming (SSW) events often lead to a cold surface air temperature anomaly over the extratropical regions. In this study, we propose, through observational evidence, that the types of SSW determine the severity of the cold anomaly. Based on the three-type classification of SSW, it is found that the surface air temperature drops notably over central to eastern North America following an SSW-type transition, especially from displacement to split. Note, however, that the differences in mean surface air temperature anomalies between SSW types are not statistically significant, even though after SSW-type transition from displacement to split, surface air temperature anomalies are colder than the other two types. The development of an anomalous tropospheric ridge in the North Pacific Arctic sector, associated with the difference in the vertical and zonal propagation of planetary waves, characterizes the post-warming period of the displacement–split type. After the occurrence of the displacement–split type transition of SSW events, upward propagation of planetary waves of zonal wavenumber 1 is suppressed, whereas planetary waves of zonal wavenumber 2 increase in the troposphere. Accompanying the ridge in the North Pacific, a trough developed downstream over North America that carries cold polar air therein. The results in this study are relevant for the subseasonal time scale, within 20 days after an SSW occurrence.