It's actually not bad at all! You need studded tires so you don't slip on ice, but generally the streets are clear and you aren't riding on too much ice or snow. And the cold is less of a problem than you might think. You need gloves, but you build up so much body heat from cycling that a heavy winter coat is too much.
The biggest problem is that subzero temperatures can make gear and brake cables freeze if there's any kind of hole in the casing. For that reason a lot of people use single-speed bikes in the winter. It's also necessary to clean and oil your bike very frequently because road salt can wreak havoc.
Personally, I can't be bothered with changing my tires or doing extra maintenance, so I leave my bike at home from mid-December to mid-March. But I just bought a Dutch-style omafiet, a very simple but sturdy bike with coaster no gears and coaster brakes, which I hope will be a reliable low-maintenance option for next winter.
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