If you ride without studs and suspect any ice, you should consider slowing your speed way down and anticipating a possible fall. Think about how you want to go down before it happens. I haven't gone down recently, but I remember a long time ago when I used to ride a long paper route 365 days a year, I went down a couple of times and it was no problem because I was going super slow and didn't try to break my fall with my wrist, etc. Went down on my shoulder at low speed. Plus, I was young and invincible.

I haven't tried the ski method, that sounds worth considering if you have to ride on ice and have no studs.

I'm riding my first pair of studded tires this winter. They take a lot of the worry about ice away, but they add a lot of rolling resistance. I've had to reconsider riding on windier days because the wind + winter tires makes it a real grind.

Good luck!