Is it worth bringing a heavy parka from home?

Yes, if it is waterproof. A dry coat is a warm coat. If your coat is only water-resistant, you will get wet when it snows and be miserable all day.

Will I need spikes for my shoes?

Yes. Pack a pair of removable ice cleats (crampons) for your boots. City sidewalks in Scandinavia turn into sheets of ice by mid-winter.

How to Pack for a Scandinavian Winter

Pack using a strict three-layer system consisting of a merino wool base, a fleece or wool mid-layer, and a windproof/waterproof outer shell. Prioritize thermal accessories like wool socks and a heavy-duty beanie, as these make the difference between misery and comfort in sub-zero temperatures.

Master the base layer. Bring two sets of high-quality merino wool base layers (top and bottom). Do not pack cotton; it holds moisture and will make you freeze the moment you stop moving.
Select your mid-layer. Pack a thick wool sweater or a high-loft fleece. This layer traps heat. Ensure it is roomy enough to fit over your base layer without restricting your circulation, as blood flow keeps your extremities warm.
Choose the right outer shell. You need a coat that is both windproof and waterproof. It should be long enough to cover your thighs and have a deep, lined hood. Test the zipper while wearing thick gloves; if you can't operate it easily, don't bring the coat.
Protect your feet. Wear boots with a thick rubber sole to insulate you from the frozen ground. Ensure they are one size larger than normal to accommodate two pairs of wool socks without cutting off circulation.

Is it worth bringing a heavy parka from home?: Yes, if it is waterproof. A dry coat is a warm coat. If your coat is only water-resistant, you will get wet when it snows and be miserable all day.
Will I need spikes for my shoes?: Yes. Pack a pair of removable ice cleats (crampons) for your boots. City sidewalks in Scandinavia turn into sheets of ice by mid-winter.