Olivier pointed to me that ESA's ground segment, PEPS and MUSCATE were all in really good shape today... And the sky was clear yesterday at the time of the Sentinel-2A acquisition!
So I could download the Level-2A product from theia.cnes.fr, run our let-it-snow processor, start QGIS and here it is: the map of yesterday's snow cover area at 20 m resolution. If you know the region, you might notice that there is currently a big contrast in the snow cover extent between the French and the Spanish Pyrenees. This is due to the blocking of the moist air masses coming from the north.
Stay tuned! Theia should start to distribute these Sentinel-2 snow products in near real time very soon.