Since it hasn't been mentioned yet: switching to a lower gear (1 or 2) can help in this situation, too. It gives you more control over the vehicle on icy roads.

I grew up and learned to drive in the snow belt. When I know roads might be icy I deliberately try to avoid stop signs/traffic lights at the bottom of a hill. Best bet is to take a different route. Skilled driving can only help so much in icy conditions.

That sounds like black ice. Nothing you can do.