I haven't done this but it might be worth looking at what mountain bike riders wear in the winter, assuming they don't stop riding. They're likely wearing things which climbers (in the winter) and skiers would wear.

... or just people in finland who ride bikes all year round.

Sure it can suck to ride your bike on a cold wet day like we get in Seattle, but the right gear can help a lot... and I'm not sure anyone is saying, "If you buy a bike you MUST sell your car and do everything on the bike". I'm taking the bike as a challenge to myself, trying to do all I can on it. But if one day I'm just not up for it or it's just pouring, or the load is to big or too far. That's what car share is for. If everyone did similar we'd have a lot more pleasant cities.

Mountain riders wear almost nothing on winter, but gloves.

Good gloves for ski or bike are inexpensive. You just need to think to buy them.

If it's really cold when you commute, just a pair of jeans and any sweater or jacket is ok, as you're cycling anyway.

But when it's raining or wet, you would rather just stay at home, get your car, or wear shorts if you're already outside.

And when it's hot, still shorts , but get a bottle of water. The biking will make a light breeze to cool you down.

But it's still up to you to find what you like.

For example, some persons do need beanies too, while others will be on beach outfit all year long.

Do "right clothes" save you from slipping on the ice?

No, but studded tyres do.

no, but snow plows and salt on roads do. also it's not like ice is instant death for a bike. it's only a problem if you brake or turn suddenly. with a little bit of care biking in ice is avoidable

The right clothes works great when you're going to the gym. When you're going to work though it is extremely difficult to not end up sweaty, and many offices don't have showers.