... I can imagine that winters there will be quite cold, with those chilly winds blowing across the Sea of Japan from Siberia. ...
Really only down to freezing, with maybe the odd overnight low going to -1 or -2. Some might say that it's a wet/damp cold, that makes it unpleasant. Winter is wet and messy--since the ground isn't cold enough, the snow melts on contact, but then since it's snowing enough it does begin to accumulate, with a wet layer on the bottom (melting off the bottom), the speed of that melting being overwhelmed by more snow on top (=heavy to shovel). Many roads have sprinklers built in, spraying water, which helps against the accumulation, but also makes it all a slushy mess. The best footwear is waterproof rubber boots, calf high (also known as wellies, if I've got that right). There's more precip in winter than the summer 'rainy season'.
Smallish storm cells blow in from the ocean, and when driving somewhere it can be snowing a lot one minute, then stop the next. Those cells often create versions of snow mixed with lightweight hail (pelletized snow, not as solid/heavy as true hail): あられ. Or that mixed with rain, みぞれ.
Also,
thundersnow (even a mention of kanazawa there). Along with snow, those cells can produce a lot of lightning and thunder. It can get pretty wild sometimes, def equal to or worse than spring thunderstorms in the US midwest.