Late November and early December is the usual time of ski resort openings. If there is a larger snowfall in mid November, many ski resorts open earlier to the joy of powder-hungry skiers. If there is not much snow there is no need to worry, though.
There are 34 skiing destinations in the Alps where you can ski at an altitude of 3000 metres or higher. That means that signifficant parts of these ski resorts are located higher than 2200 metres above sea level. This provides virtually 100% guarantee of good skiing conditions in early December, all due to snowmaking possibilities. If temperatures are low the snow gets made and skiing is possible.
By mid December all ski resorts are usually open and the last week before Christmas is one of the best times to go skiing. The slopes are empty, the temperatures are low which ensures excellent conditions and you can still get up to 8 hours of skiing each day (lifts operate 8am-4pm). Accommodation prices are low so you can take advantage of a comfortable hotel stay at a price of a self-catered apartment.
Italian ski resorts use December to lure skiers with their popular Free Ski offering. Livigno is the most popular Free Ski destination, but Val di Sole and Bormio have their fans, too.