The Swedes have a phrase, "Ska vi fika?", which translates literally as: "Shall we have a coffee break?" But it denotes an awful lot more than that. It's a heartily embraced cultural tradition involving friends, coffee and a cosy corner in a warm cafe.

"It's a social thing. You can have a fika on your own but it's more about getting together, chatting, catching up," explained Lena Larsson, a Gothenburg native who first introduced me to the concept.

Gothenburg is a cold and windy coastal city, sitting at the mouth of the Gota river, equidistant from Copenhagen and Oslo. Its history is of trade and heavy industry – Volvo and Ericsson have factories in the area. A network of canals, created by Dutch city planners in the 17th century, crisscross the city, leaving big open areas for winds to whistle down. So the locals know a thing or two about keeping warm.

Lena's enthusiastic adoption of fika means when she walks into Mauritz's café on Fredsgatan she orders "a number six" – coffee with an apple cinnamon bun – rather than going through the long process of actually reading the menu.

"Gothenburg people are so happy and open," said Annika Larsson (no relation to Lena) who edits ilovegoteborg.se. We were enjoying our first fika of the day, sitting wrapped up against the cold outside Cafe Kronhuset (cafekronhuset.se), on a peaceful, cobbled square in the oldest part of Gothenburg. "It's great in winter because it looks so pretty and there are so many places you can go indoors to sit, have a coffee, and watch the world go by."

First stop on our fika tour was Haga. The area is hailed as the arty, bohemian heart of Gothenburg, with pastel-coloured buildings lining its three main cobbled arteries. In truth it embraces bohemia in a very refined, very Swedish way, vintage hat stores and jewellery shops mixing with chilled-out cafes. Stepping into Café Kringlan on Haga Nygata was like getting a big hug from a slightly overweight farmer's wife clad in head-to-toe Prada. The cafe is immaculate in its cosiness – cinnamon buns beautifully laid out on the counter, the lattes a swirling work of art. Two girls were sitting in a corner laughing and gossiping.

Equally enticing, to the left of Café Kringlan, is Le Petit Café, a coffee shop sweet enough to cause your teeth to fall out on entry, with pastel-coloured blankets for those sitting outside to wrap themselves up in.

Two buns down and it was time to move on. I took refuge in Cigarren, a café with a masculine colour scheme – brown – and a floor-to-ceiling humidor. Clearly pastry was not this place's raison d'etre, which gave my blood sugar levels time to realign themselves. I had a thick espresso while watching well-dressed Swedes stride across lively Järntorget square. I could have stayed people-watching all day, but dragged myself away to look at the ornate Oscar Fredriks Kyrka, a neo-gothic church nearby on Prinsgatan.

It was a short walk from here to a slightly grittier part of town known as the "long streets" or Langgatan. Here tattoo parlours, punk shops and grand brownstones replaced pastels. In Dirty Records, the smell of dusty vinyl combined with the aroma of coffee from the in-store cafe. It has everything a record shop should have – scuffed lino, piles of obscure albums, a man with an impossibly large quiff sitting behind the front desk. I supped a latte while discussing the merits of Matthias Hellberg & the White Moose versus the Jelly Bean Bandits with quiff man. After so much caffeine he became my new best friend.

For those after a slightly different kind of fika, Café och Konsthantverk, across the street, has multicoloured lights, huge cushions 1960s–style wallpaper (and an art gallery).

Gothenburg is shedding its industrial past and embracing a future filled with contemporary art and fashion-forward thinking. But I was keen to get a feel for the city away from the picture-perfect bohemia of both Haga and Langatan, so headed out to Majorna, a residential district. Busy roads gave way first to Soviet-style apartment blocks and then to avenues filled with art bookshops and crisscrossed by tramlines and lined with trees.

Men in overalls and boots were piling into Cafe Skogan on Mariaplan, the smell of steam and grease mixing with the salty Gothenburg air when they opened the door. Further on, on the wide open Mariagatan, Kafé Marmelad (kafemarmelad.se) has huge pots of geraniums, a red and white check floor and chunky mugs creating a warm, homely atmosphere. Kissing goodbye to my hip bones I had another bun and another latte, hunkering down at a window seat to watch the low sun recast the view in gold.

My final bun of the day was in Soppakaffe, further down Karl Johansgatan. I sank into the sagging velvet sofa and caught sight of myself in a huge gothic-style mirror, my eyes wide. Cripes, no more caffeine for me, I thought, and felt I wouldn't want to see another cinnamon bun as long as I live.

But as long as you don't pack more than a couple into one day, embracing the fika concept is a sure bet for warding off the winter.

• The Avalon Hotel (+46 31 751 0200, avalonhotel.se) has doubles from around £150 a night. Flights to Gothenburg booked with Expedia.co.uk (with easyJet from Gatwick, Scandinavian Airlines from Heathrow, Ryanair from Stansted and Glasgow, City Airline from Birmingham and Manchester) start from £38. For more information see visitsweden.com