I've managed every day for the past 2 winters both on a hybrid. As a wimp, I do not subscribe to the just get thicker socks theories. I've got everything I can get my hands on.
Bike: yes to muguards; most big tyre makers have winter recommendations. I used specialized - but not on a road bike. Keep as clean as you can. Get a decent lube - I use purple extreme. The salt is vicious.
Weather: Harder. You need to balance wind, water and cold protection against comfort when exerting yourself. I've spent quite a lot on clothes, but when I started I got most of my cheap from Lidl, Aldi or Tchibo. Their stuff is more than adequate, and really cheap. You'll need base layers, shirts and a jacket. Aldi did some great trousers last winter with water resistant panels at the front. I use rainlegs - I found that waterproof trousers made me wet with sweat faster than the rain. But wet thighs are worse than uncomfortable! Most of the water comes up from the road rather than down from the sky, so get used to wet calves!
If you are going to spend a little bit of cash I'd go for some decent gloves and overshoes or waterproof socks. Before I got clip in pedals, I wore light walking boots which kept me dry. Toasty fingers and toes will make everything else seem bearable. If you're absolutely certain you're going to keep going all winter, a merino will base layer is worth it. They stay warm even when wet, wick sweat away from the body really well and don't smell! Howies have some in their sale at the moment for about £35.
Some sort of under-helmet protection against cold and water would be good. I use a buff until it gets really cold. I've got a Tchibo hat £3 which did the trick when it was really cold or pouring down. Buffs are great for covering exposed areas between top of shirt and head.
Safety: Decent lights so they can see you. I got a Foska bones jacket for Xmas my first year and on-coming traffic imediately slowed and dipped headlights. Even more dramatic was the effect of flashing reflective armbands from Aldi: at £2, the best buy I've made. The worst thing about winter commuting is idiots who drive towards you at full beam, so some glasses with a slight tint even at night are essential for me on country roads.
Enjoy!