Bridges and overpasses are what you need to worry about. I skip cycling when there is ice on the road or potential for it. We don't get enough icy weather in NC to invest in studded tires, and it's not worth the risk trying to cycle on icy streets in my book.

BTW, I rode to a group ride on Sunday a couple of weeks ago, when we had clearing rain, wet roads and temperatures hovering near freezing. It was about 33 F when I left home about 9 am, and I expected the temperatures to start rising. Instead, the temperatures kept falling and it was probably around 30 F when I reached the park where our rides start. I hit a patch of ice in the park, which caused my rear wheel to slide but I didn't fall. That made rest of my ride pretty sketchy at best. Although I didn't hit any more ice, I was totally paranoid the entire ride, particularly on bridges and shady downhills. I won't do that again.