Do I really need specialized winter boots?

Yes. Sidewalks in Scandinavian cities are often treated with gravel rather than salt, and compacted snow turns into ice. Fashion boots with smooth soles will result in a fall.

Is it better to wear many thin layers or one big coat?

Layers are superior. You will be moving from -10°C outside to +22°C inside shops and museums. Being able to unzip or remove a layer prevents you from overheating and sweating, which causes chills later.

Mastering the Scandinavian Winter: A Packing Strategy

Dress in three distinct layers: a moisture-wicking base, a heat-trapping mid-layer, and a windproof/waterproof outer shell. Prioritize wool over cotton and pack sturdy, waterproof boots with aggressive traction to handle packed snow and ice.

Choose your base layer. Bring 3 sets of merino wool base layers (top and bottom). Merino wool is essential because it regulates temperature and doesn't hold odors like synthetic fabrics. Avoid cotton at all costs; if it gets wet, it will stay cold and damp against your skin.
Select your mid-layer. Pack one thick wool sweater or a high-quality fleece for insulation. This layer traps your body heat. If you're going to the Arctic Circle, bring two—one to wear and one as a backup.
Pick the right outer shell. You need a parka that is windproof and water-resistant with a hood. Ensure it is long enough to cover your hips. If it doesn't have a down or synthetic fill, you will need a separate insulated puffer jacket to wear underneath it.
Prioritize footwear and extremities. Pack one pair of waterproof, insulated boots with rubber lug soles for grip. For extremities, bring two pairs of thick wool socks, a windproof beanie that covers your ears, a neck gaiter (buff), and touchscreen-compatible thermal gloves.

Do I really need specialized winter boots?: Yes. Sidewalks in Scandinavian cities are often treated with gravel rather than salt, and compacted snow turns into ice. Fashion boots with smooth soles will result in a fall.
Is it better to wear many thin layers or one big coat?: Layers are superior. You will be moving from -10°C outside to +22°C inside shops and museums. Being able to unzip or remove a layer prevents you from overheating and sweating, which causes chills later.