We find that simulated stratospheric sulfate geoengineering could lead to warmer Eurasian winters alongside a drier Mediterranean and wetting to the north. These effects occur due to the strengthening of the Northern Hemisphere stratospheric polar vortex, which shifts the North Atlantic Oscillation to a more positive phase. We find the effects in our simulations to be much more significant than the wintertime effects of large tropical volcanic eruptions which inject much less sulfate aerosol.