Snowfall is an important element of the climate system, and one that is expected to change in a warming climate(1-4). Both mean snowfall and the intensity distribution of snowfall are important, with heavy snowfall events having particularly large economic and human impacts(5-7). Simulations with climate models indicate that annual mean snowfall declines with warming in most regions but increases in regions with very low surface temperatures(3,4). 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 overmany Northern Hemisphere land regions. For example, for monthly climatological temperatures just below freezing and surface elevations below 1,000 metres, the 99.99th percentile of daily snowfall decreases by 8% in the multimodel median, compared to a 65% reduction in mean snowfall. Both mean and extreme snowfall must decrease for a sufficiently large warming, but the climatological temperature above which snowfall extremes decrease with warming in the simulations is as high as -9 degrees C, compared to -14 degrees C for mean snowfall. These results are supported by a physically based theory that is consistent with the observed rain-snow transition. According to the theory, snowfall extremes occur near an optimal temperature that is insensitive to climate warming, and this results in smaller fractional changes for higher percentiles of daily snowfall. The simulated changes in snowfall that I find would influence surface snow and its hazards; these changes also suggest that it may be difficult to detect a regional climate-change signal in snowfall extremes.