We analyzed output from the Geoengineering Model Intercomparison Project for the two most “realistic” scenarios, which use the representative concentration pathway of 4.5 Wm−2 by 2100 (RCP4.5) as the control run and inject sulfate aerosol precursors into the stratosphere. The first experiment, G3, is specified to keep RCP4.5 top of atmosphere net radiation at 2020 values by injection of sulfate aerosols, and the second, G4, injects 5 Tg SO2 per year. We ask whether geoengineering by injection of sulfate aerosols into the lower stratosphere from the years 2020 to 2070 is able to prevent the demise of Northern Hemispere minimum annual sea ice extent or slow spring Northern Hemispere snow cover loss. We show that in all available models, despite geoengineering efforts, September sea ice extents still decrease from 2020 to 2070, although not as quickly as in RCP4.5. In two of five models, total September ice loss occurs before 2060. Spring snow extent is increased from 2020 to 2070 compared to RCP4.5 although there is still a negative trend in 3 of 4 models. Because of the climate system lag in responding to the existing radiative forcing, to stop Arctic sea ice and snow from continuing to melt, the imposed forcing would have to be large enough to also counteract the existing radiative imbalance. After the cessation of sulfate aerosol injection in 2070, the climate system rebounds to the warmer RCP4.5 state quickly, and thus, any sea ice or snow retention as a result of geoengineering is lost within a decade.