The stratosphere can have a significant impact on winter surface weather on subseasonal to seasonal (S2S) timescales. This study evaluates the ability of current operational S2S prediction systems to capture two important links between the stratosphere and troposphere: (1) changes in probabilistic prediction skill in the extratropical stratosphere by precursors in the tropics and the extratropical troposphere and (2) changes in surface predictability in the extratropics after stratospheric weak and strong vortex events. Probabilistic skill exists for stratospheric events when including extratropical tropospheric precursors over the North Pacific and Eurasia, though only a limited set of models captures the Eurasian precursors. Tropical teleconnections such as the Madden‐Julian Oscillation, the Quasi‐Biennial Oscillation, and El Niño–Southern Oscillation increase the probabilistic skill of the polar vortex strength, though these are only captured by a limited set of models. At the surface, predictability is increased over the United States, Russia, and the Middle East for weak vortex events, but not for Europe, and the change in predictability is smaller for strong vortex events for all prediction systems. Prediction systems with poorly resolved stratospheric processes represent this skill to a lesser degree. Altogether, the analyses indicate that correctly simulating stratospheric variability and stratosphere‐troposphere dynamical coupling are critical elements for skillful S2S wintertime predictions. Key Points Tropospheric precursors of SSW events are better represented for the North Pacific than for Eurasia Teleconnections from the tropics add probabilistic skill but are only represented by a few models Weak and strong vortex events in the NH stratosphere can contribute to surface skill 3–4 weeks later