Whereas changes in magnitude of geophysical extremes under climate change have received significant attention, potential concomitant changes in spatial dependence structures have remained unexplored so far. Here we provide first evidence of such an effect, highlighting a significant trend in the spatial dependence structure of snowfall extremes in the French Alps at decadal time scale. Specifically, we process a comprehensive data set of winter maximum snowfall from all over the French Alps collected in 90 stations from 1958 to 2012. We estimate extremal dependence over 20year moving estimation windows taking into account possible anisotropy potentially related to orographic effects and/or patterns in atmospheric flows. For each window, we derive a range representing the distance above which extremes are almost independent. We show that snowfall extremes tended to become less spatially dependent over time, with the dependence range reduced roughly by half during the study period. We demonstrate the connection between this trend and local and synoptic climatic variables associated with the current climate change context. In details, the decreasing pattern in extremal dependence is concomitant with a trend toward less harsh winter conditions. It is attributable at first to the increase in temperature and its major control on the snow/rain partitioning. Yet a magnitude effect, with less dependent extremes due to a decrease in intensity of precipitation, also exists. Finally, we show that our results are largely insensitive to the minimal modeling assumptions necessary to our data-based approach. This robustness makes it potentially suitable for various other studies in the field of geophysical extremes.