It's a hard topic to handle in one thread. There's an entire forum on the subject. There's also a website that might be useful: http://www.icebike.org

You didn't say what part of the world you're in. Mountain bike tires are fine for snow (lowering the pressure helps) but don't help at all on ice. For ice you want studded tires. Having said that, there are people here who commute all year on 28c road tires. Doesn't work for me, but if the roads are cleared pretty well where you ride, you may not need to worry much about tires.

People don't all react to the cold the same way so it's hard to make universal recommendations on things like mittens or gloves. Experimentation is the key. Nature is kind in that you're not plunged from summer to winter in one day and you'll have some time to figure things out as the days get colder.

What is fairly universal though is avoiding cotton and dressing in 3 or so thin layers as opposed to a medium layer and a really bulky outer layer.

The base layer (the one next to your skin) would be something like a really good set of long underwear made out of a moisture wicking material. The middle or "warmth" layer is a bit thicker and is usually something like fleece. The outer layer is a windproof shell.

That's what I'll wear in Minnesota to give you an idea. If I'm exerting myself (like riding a bike), my hands and feet don't get too cold. A good set of skiing gloves are fine for my hands. This doesn't work for everybody. For my feet, a good set of hiking boots with wool socks work fine. A bit better is wool socks + running shoes + neoprene booties but the booties are kind of a hassle.

For my head I'll wear a thin balaclava and a helmet. If it's really cold, I'll add ski goggles.

I've never had a chain freeze and any ice that collected on it (in a freezing rain storm or something) would quickly break off once I started riding. A rusty chain is a more common problem because of the salt used here to clear the roads.

Fenders are more important in winter than in the summer.