Black ice has the strange property of being a gravity well: when your bike tires slip on it, you go down about 10x faster than normal.

Yes, studded tires (there are options other than the Marathon Winters but all are better than none), ride more slowly, stay more upright when you turn (but then, when you're riding more slowly, you're less likely to bank into a turn), avoid black ice (forehead slap!) and wear a helmet.