I was more terrified of my father sitting next to me at first, but I was still terrified every time I got behind the wheel for years after. After that, I moved to St Paul, MN. Nine months of driving in that city will teach you how to control your vehicle in ways you wouldn't think to test in a small town. We have some of the nicest drivers that I've seen anywhere (I don't travel much, but Chicago sucks), but it's still nerve-wracking.
The lesson I learned is that you have to get used to the vehicle until it becomes an extension of yourself. Your perception is extended by the mirrors, and you are now responsible for this piece of steel and plastic that you're going to hurl down the road at 60-80 mph.
As for the ice thing, find a parking lot with a good amount of ice and packed-down snow, empty, and make sure either the place is closed, or you know the staff/owners. Then take your car and practice losing and regaining control of the vehicle. Arrange tighter and faster turns until you feel the tires lose grip, then let off the gas until they grip again. Practice. Seriously.
personal gripe: use your blinkers, look before changing lanes, and don't be an asshole.
Thank you.