Local weather forecasts appear on the radio (in German, of course). In the winter, snow reports can be found (we presume). There is a local forecast on the Bad Aussee tourist office site, http://www.badaussee.net/. You can phone for a forecast (also in German) or you can try the Tourist Office in Bad Aussee (no idea if they post a bulletin in the window - we don't seem to have tried).
But for an up to the minute (maybe) idea of the weather right now, try the Loser WebCam - giving a current view of Loser from somewhere near the bottom of the ski-lifts - or (slightly further away but usually better photos - caution! These could induce an irresistible desire to drop everything and travel to Austria immediately!) the Grundlsee Photo of the Day.