One thing to understand about single track vehicles is that they steer by camber-thrust (think conical dixie cup rolling in a circle). This requires the center of gravity to be off to one side of the contact patches the tires have with the ground - and loss of traction catastrophic (i.e. an immediate fall down). Been there a number of times on a motorcycle. I was dressed for a crash; bicyclists typically are not.

TL;DR: ice is bad for bikes.