We test how the time of year of a large Arctic volcanic eruption determines the climate impacts by conducting simulations with a general circulation model of Earth's climate. For eruptions injecting less than about 3 Tg of SO2 into the lower stratosphere, we expect no detectable climatic effect, no matter what the season of the eruption. For an injection of 5 Tg of SO2 into the lower stratosphere, an eruption in the summer would cause detectable climate effects, whereas an eruption at other times of the year would cause negligible effects. This is mainly due to the seasonal variation in insolation patterns and sulfate aerosol deposition rates. In all cases, the sulfate aerosols that form get removed from the atmosphere within a year after the eruption by large-scale deposition. Our simulations of a June eruption have many similar features to previous simulations of the eruption of Katmai in 1912, including some amount of cooling over Northern Hemisphere continents in the summer of the eruption, which is an expected climate response to large eruptions. Previous Katmai simulations show a stronger climate response, which we attribute to differences in choices of climate model configurations, including their specification of sea surface temperatures rather than the use of a dynamic ocean model as in the current simulations.