The hills are alive with . . . the sound of roasting chestnuts and scent of mulling wine. Salzburg might be entwined for ever with the campest musical the world has ever seen, but tourism cannot live by kitsch alone. If summer is the time to cash in on its musical heritage with the prestigious five-week festival of classical music, for the colder part of the year this town turns into a snowy winter marketplace, all pretzels, glühwein and unfathomably colourful bobble hats.

In effect, Salzburg splits its year tidily into contrasting segments: high culture during the long summer nights, chunky knitware and Teutonic comfort food when there’s a nip in the air.

It helps that Salzburg is a pretty film-set of a town, the preserved medieval and baroque centre fringed on every horizon by the mountain ranges that inspired Mozart and, much later, Rodgers and his chum Hammerstein.

This settlement has existed for at least 16 centuries. The Salzach river runs through it, neatly dividing the town into the business region behind the Kapuzinerberg crag, and the attractive houses, churches, palaces and cobbled alleys of the old town gathered around the four squares of Mozartplatz, Domplatz, Residenzplatz and Kapitelplatz, crammed in cosily between the Monchsberg ridge and the river. The old town is a treat to walk around, from St Markus church through the alleys and squares to the Hohensalzburg fortress perched on the hill. Preservation rather than strict authenticity is the keynote. After all, Salzburg’s economy now relies heavily on tourism rather than the salt mines that originally brought the area prosperity. Mercifully, they have just finished repairing the Festungsbahn funicular to save you the punishing climb to the fortress, so you can take a comfortable ride up to Salzburg’s pinnacle, which is torn between being a dignified 500-year-old edifice symbolic of Salzburg’s history and a rather tacky theme-park evocation of medieval barbarities.

As such it’s a suitable starting point for a Salzburg visit, given that the town merrily juxtaposes the tasteless with the austere. Eventually, though, you have to face the music. Salzburg is inevitably defined by its relationship with Mozart and Maria. Wolfgang Amadeus, born 250 years ago last Friday, is somewhat incongruously celebrated by the ubiquitous chocolate and marzipan confectionery called Mozartkugel that defines Salzburg tourism in much the same way that stuffed donkeys encapsulate the Costa del Sol.

The town’s relationship with its most famous scion can occasionally seem sickly and cloying. A surprising number of locals seem to use Falco’s Rock Me Amadeus tune as their ringtone, and being Austrians, you can’t be sure they are being ironic.

The little house where the prodigy grew up, his Geburtshaus on Getreidegasse, is thronged with musical pilgrims. Classical music lovers, though, will get a frisson from seeing the instruments on which the infant Mozart bashed out his earliest melodies.

More information, more attractively presented, is provided at the composer’s family home, the Wohnhaus on Makartplatz, with plenty of audiovisual material in English as well as German. The square named after the composer is lit up with markets and an ice rink in winter, somewhat distracting from its elegance.

That egregious 1960s musical is the other substantial cultural presence in Salzburg. The four-hour tour of the Sound of Music locations remains immensely popular, with parties made up of young gay men and women of a certain age.

It should come with a health warning. This is for aficionados only as enthusiastic fans are liable to burst into off-key renditions of the twee tunes at every opportunity. The composers could never have realised that “Doe a deer” was a musical phrase capable of inspiring a homicidal impulse when you hear it for the 14th time in an afternoon.

Maybe even the locals are beginning to weary of the musical. I spot a nun coming down the Kapitelgasse, and the expression she shoots back is one of “Yeah, I’m a nun in Salzburg, and no, I’m not about to burst into song”.

A rather classier attraction for music-lovers is Oberndorf, a short train ride away. This unremarkable village is where the composition of the world’s most popular carol, Stille Nacht (Silent Night), took place, bashed out on a productive Christmas Eve in 1818 by Franz Xavier Gruber (tune) and Joseph Mohr (lyrics), the Elton John and Bernie Taupin of their day. Visit during the festive season and you’ll hear the local choir honing their spine-chillingly pure rendition.

This is one of several rewarding day trips within easy reach of the town. The ski crowd head for Zell am See or Kaprun, worth visiting out of season when the streets aren’t thronged with loud piste parties. Even if you come without the Lycra and mirror goggles, it’s worth seeing the glorious peak of Kitzsteinhorn on a clear afternoon, about 10,000ft up, pure white against a deep blue sky, the colours a natural rendition of a Scotland football strip, only more moving.