Any reduction in global mean near-surface temperature due to a future decline in solar activity is likely to be a small fraction of projected anthropogenic warming. However, variability in ultraviolet solar irradiance is linked to modulation of the Arctic and North Atlantic Oscillations, suggesting the potential for larger regional surface climate effects. Here, we explore possible impacts through two experiments designed to bracket uncertainty in ultraviolet irradiance in a scenario in which future solar activity decreases to Maunder Minimum-like conditions by 2050. Both experiments show regional structure in the wintertime response, resembling the North Atlantic Oscillation, with enhanced relative cooling over northern Eurasia and the eastern United States. For a high-end decline in solar ultraviolet irradiance, the impact on winter northern European surface temperatures over the late twenty-first century could be a significant fraction of the difference in climate change between plausible AR5 scenarios of greenhouse gas concentrations.