I regularly commute in the winter, about 11 or 12 miles each way.
For the winter it's safest to run at least two taillights (planet bike superflash turbos are great for this), one in blinking mode and one steady. I've had taillights fail, and you don't want to be riding in the dark while invisible to cars. You can use AAA rechargable batteries in them, and they last a long time. I used to run a rechargable AA battery headlight, but they just don't make any that I think are bright enough for when it's really pitch black. My preference is for a high lumen USB chargable headlight. The Cygolite Metro 750 is a great choice. You'll need to remember to charge it regularly though.
Clothing-wise - layers. Get a very bright neon coloured windshell with some reflective accents. Then you just add various layers beneath it depending on how cold it is. I'm a fan of synthetic fleeces for sweat wicking and warmth. Make sure there are zips for venting . . . because you'll get your clothing wrong from time to time and it'll help keep you from cooking. Beneath that I like to have something sweat wicking and skin tight (underarmour type shirts). I've got a couple pairs of heavy weight winter tights that I think were designed for skiing which work well on my legs. Below freezing, you should cover your face with some kind of mask to avoid frostbite. A thick pair of overgloves with a thin pair of gloves beneath that will keep your hands warm, and (taking off the big gloves) will allow you some dexterity for doing things in the cold like locking up. Get footwear that is a size or two too big for you to make room for thick/heavy socks. Thick wool socks (two pairs if you can swing it) will keep your feet warm through a lot of cold weather. Tight shoes (no matter how warm) will reduce circulation and your toes will get frostbite, so make sure you try on your shoes/boots with the heavy socks you're going to be wearing. A thin toque or headband is usually good on your head. When it's really cold, taping over the vents in your bike helmet will keep your head much warmer. ALWAYS wear glasses/goggles over your eyes in the cold . . . otherwise you'll be tearing up non-stop when you get going.
Tires-wise, it's very dependent upon where you're cycling. I ride on the road, and they're very aggressive about salting here. I'll often be riding through snow/slush but there's rarely any ice. I like 28 mm tires with some grip for snow/slush. They punch through to the ground beneath, and roll much better than wise mountain bike type tires. You need some grip though, because loose snow is too slippery otherwise. If you live somewhere that there's lots of ice, it's probably worth getting studded bike tires - just be aware that they are extremely slow whenever you're not cycling on ice.
Most important is to be flexible in the winter. There have been times when I got out on the roads before the plows on certain streets and I've had to shoulder my bike because it was too slippery to ride. Know your route (some areas will reliably be slippery or are places that ice builds up - it's good to know where these are). Reduce your speed when going down hills. Stop early for stop signs and lights. Change lanes early. Take the lane when you need to. Be very careful using your front brake or turning your handlebars if you're on loose/slippery stuff - it is easy to wipe out (I'd recommend that you spend a couple snowy weekends playing in a parking lot to get a feel for how your bike handles in snow and on ice - you don't want to learn this in the middle of the road). If the weather is really bad (like freezing rain) leave the bike at home . . . that type of weather doesn't happen often enough to be worth risking your life.