I would never tolerate falling down regularly. Studded tires work extremely well. I ride through blizzard and on ice and slush without any trouble. The only time I went down due to ice was riding on a frozen puddle where my tires gripped the ice but the ice didn’t grip the ground under it. That was a decade ago.

Breaking a wrist or collarbone (or worse) happens far too easily to just accept routine crashing.