The Arctic stratospheric polar vortex (SPV) is known to influence winter surface climate through dynamical coupling. Here, we demonstrate that beyond this established pathway, variations in SPV strength also modulate Arctic high clouds, inducing persistent radiative effects at the surface. This previously less well recognized mechanism shows that a strengthened SPV increases Arctic high-cloud cover, generating a positive net cloud radiative effect that amplifies Arctic Ocean warming and sea ice loss over the Barents-Kara Sea; a weakened SPV produces opposing effects. Our results establish this radiative pathway as one of the primary drivers of the winter-mean Arctic response to stratospheric variability. Numerical experiments confirm that this radiative pathway can cause up to 1.7 K of Arctic Ocean warming during the delayed phase of strong SPV events relative to climatology. Notably, the radiative influence operates more persistently than the transient dynamical response, offering enhanced predictive potential for subseasonal-to-seasonal Arctic surface conditions. These findings reveal a key radiative mechanism underlying SPV-driven Arctic climate variability, which is essential for understanding present and future winter Arctic changes.