Well, at least your child had been delivered to school, so can still retain youthfull illusions about the infallability of parents, for a bit longer. And without injuries that would bring you to the attention of social services. It is worth remembering that the roads in the city that get gritted on icy mornings are the main roads, the ones with heavy motor traffic, not the quiet back roads used by bikes. The offroad paths are usually ok, but where cars go they can make things slippery. Station Road from Ashley Hill road down to the footpath under the railway line is particular entertaining in winter -you can get very hurt here without even trying.
This raises a question about safety wear. Not the "helmet question", that being the religous war that tears bicycle mailing lists apart. Something better: the Body Armour question. Knee and elbow pads have trickled over from Downhill MTB to cross country. Because it is quite pleasant to not be bruised and scarred after a day in the woods. The Body Armour question extends this to commuting in winter. Given that when you come off a bike, its your elbows, hands and knees that usually hit the ground first, should you wear body armour on the cmmute -if you already own some? Or should people find routes to school and work that aren't so icy?