The goal of this work is to investigate and explain recent trends in total yearly snow-depth and maximum yearly snow-depth from daily data in light of both the current global warming and the low-frequency variability of the atmospheric circulation. We focus on the period 1979–2018 and compare two different data-sets: the ERA5 reanalysis data and the E-OBSv19 S precipitation data, where snow-depth is identified from rainfall by applying a threshold on temperature. On one hand, we show that the decline in average snow-depth observed in almost all European regions is coherent with the mean global warming and previous findings. On the other hand, we observe contrasting trends in maxima. We argue that this apparent discrepancy between trends in average and maximum snow-depth comes from the subtle effects of atmospheric circulation in driving extreme events and the non-trivial relation with global warming: a warmer Mediterranean Sea may enhance convective precipitation in winter-time and trigger heavy snowfalls. We discuss the limitations of block-maxima indicators and of static identification of trends based on regional or grid-points analysis, paving the way for attributing changes in extreme snowfalls via analogs-based methods.