Really nasty conditions on a hill

It was about -5C today, so most of the bikeways were dry/frozen, except some spots where sun was getting through. A Really Nasty spot was on a hill today. At the bottom of the hill the bikeway is solid ice and the ice has some grooves on it but one can cycle on it. The first photo is about half way up:

I pocketed my camera and continued uphill until the rear tyre started to slip and I decided it was better to walk the last few meters. Just look at this shiny, smooth ice:

The very top of the hill is not shadowed by trees or buildings, meaning the sun will start to melt the ice first there. The water will run downhill, get to a more shadowed spot and freeze. The gritting sand sinks into the ice (or gets covered by ice) and the frozen run-off is really smooth. Very slippery!