Snowfall is an important element of the climate system, and one that is expected to change in a warming climate. Both mean snowfall and the intensity distribution of snowfall are important, with heavy snowfall events having particularly large economic and human impacts. Simulations with climate models indicate that annual mean snowfall declines with warming in most regions but increases in regions with very low surface temperatures. The response of heavy snowfall events to a changing climate, however, is unclear. Here I show that in simulations with climate models under a scenario of high emissions of greenhouse gases, by the late twenty-first century there are smaller fractional changes in the intensities of daily snowfall extremes than in mean snowfall over many Northern Hemisphere land regions.