If you are in Central Europe during the Winter months (northern hemisphere) you should make every effort to spend a few days in one of the most charming places I would choose for a European Winter experience that does not necessarily have to involve skiing.
Whether you go ice skating on the "Mozart Platz" in the center of the city, have mulled wine, take a stroll on on of the mountains in the middle of the city, which gives you magnificent views, or want to breath some thousand years of history, baroque style, music, arts, or museums, Salzburg is probably one of the most exquisite places I have been to.
If you want organized travel, there are bus trips to surrounding areas and sites available starting from the Mirabell Platz, a square in front of the Mirabell Schloss, about 5 minute bus trip from the main train station. The same Schloss Mirabell (a baroque castle with beautiful gardens, outdoor theater stage, maze of hedges, fountains, and statues depicting classical Greek mythology) also features top quality classical concerts (Salzburger Schlosskonzerte) in its Marmor Saal (marble hall), a hall with walls and floors entirely made of marble, which is used during the day time to conduct weddings in the most romantic setting.
Most importantly I would like to mention that the prices, compared by international standard, are very affordable. This goes for hotels, restaurants, concerts, museum admissions, etc.
A word about restaurants: Austrian gastronomy needs special mention, as besides formal restaurants for eating out, or coffee shops where one would mainly have a hot drink with one of the irresistible slices of cake, there are also Tavern-like places, where one can eat full meals, or just choose to have a glass of beer or wine, a spirit, a bowl of soup, franks, crepes, or whatever else the menu offers.
The most unusual feature of these places is that one can sit there alone, with a friend, or in larger company, over a cup of coffee or a glass of beer, and enjoy the atmosphere without feeling that one has to leave within a short time.
I used to go to the so called "Müllner Bräustübl" a large brew house where they serve great beer in big ceramic steins, and sit there over one beer for an hour or two, without being 'molested' by waiters. In smaller taverns (Gasthaus) the waitress or the waiter will approach the guests, when they see that the guest finished his/her drink, but only out of courtesy to find out if you want something else, and not in a pushy manner.
Again, the pricing in all the places I have been to was very reasonable.
I experienced New Year's Eve in Salzburg, which was an amazing event, with people - equipped with fireworks and champagne bottles - were packed in the city center as well as on the city mountains, from which most of the fireworks were launched. However there was a small disappointment: The fireworks started so early, and in such great numbers, that the old city was veiled in smoke by the time midnight came around. It also was extremely crowded, but due to the frosty weather this didn't feel oppressive. People in general were very friendly, happy, and disciplined that night.
I would like to suggest a beautiful walk along the Untersberg, Salzburgs highest mountain in the closer vicinity to the city.
It is a 15 minute drive in direction of Großgmain, with a forest road, closed to regular traffic, going along the mountain in a magic setting of snow laden trees and mountains. At the end of the valley one reaches "Wolfsschwang", and gets rewarded with the sight of a herd of deers that is kept in a large enclosed area there. A wooden cabin has a coin slot on one of the outside walls and when inserting 50 Eurocent, deer fodder is being ground, and falls into a bucket, which can be taken to feed the deers.
Most importantly, - the tourist masses are only in the city center, and when venturing onto one of the mountains, or into some old side street, one always can find quite recluse in order to just soak in the atmosphere.