I rode up one morning, stopped, hopped off the bike and promptly fell down. It was too slippery to stand, yet, I'd just ridden across it, just fine. That's when I knew I'd made the right decision on studs.
Yep! I've had similar things happen to me. It is downhill from my house into town. It is often safer to ride than to try to walk without falling. In general, I have learned to be extra careful when dismounting from the bike.
Studded shoes. Now that's what I need.
(One of my neighbors races motorcycles on ice during winters. You should see the serious studs that he's got on his machine. They stick out quite a bit, maybe 3/8s inch or so, but only on one side of his tires. Why only one side? The courses are all circular, and always in the same direction.)