The summer high season is in July and August, when crowds will be bigger and prices higher. The heat can be very uncomfortable during the summers in the cities. Some institutions also will close down during these months. During the winter months, the cities will be less crowded and prices in general for hotels will be lower
Winter sports are in full mode from mid-December to late March with the high season over Christmas, New Year and February. The Alpine resorts can be very quiet from late April to late May and in November.
Spring in the Alps is in June, when the Alpine flowers start to bloom.
In the beginning of the new year the 4 Schanzen Tournee of the skijumpers takes place in Germany (Obersdorf, garmisch) and Austria (Innsbruck, Bischofshofen). I would like to go there and watch that championship!