Here's a great example of what happens when it's icy and you keep plenty of distance between you and the car you're following, and what happens when you don't.

Here's the video uploader's explanation of what happened, as pulled from this LiveLeak link.

This was me coming back to Ontario,Canada from NY state. Started braking 12seconds into the clip, fully loaded with 6 giant paper rolls and at max load weight. It might seem like I was braking normally, but I wasn't. Truck's ABS was working and I was pressure braking in and out every second, if i wasn't i would jackknife or slide trailer into opposite lane. Either way, my day went well, unlike for other drivers on the road.

The examples here involve big rig trucks, but they hold true for everyone on the road. Don't tailgate in bad weather, people.