I drive and cycle.
Cycling on the pavement is not a good idea. It is too slow, dangerous for pedestrians and illegal.
Cycle on the road, but a good distance from the kerb - approx 1m, so that you don't bang into drains and can wobble up hills. Keep a steady speed, look around you and remember that cyclists make some car drivers nervous.
If it is icy the best things you can do are check your brakes, make sure your tyres are fully inflated and have sufficient tread, drive more slowly. If you encounter black ice, it's probably best to dismount. And wear gloves too!
Cycle paths are good: cycle lanes can be a curse - particularly as you have to move in an out to accommodate parked traffic.
In terms of good behaviour, don't take the piss by jumping lights, not signalling, going without lights. It justs pisses off people who we need to share the road with.
There are lots of daft people who use bikes. Not outnumbered by daft drivers who routinely brake speed limits, fail to signal, use their horns for sport or park in cycle lanes.
As a cyclist my biggest bugbear with drivers is failing to signal. I understand that people think that road position means that they don't need to signal (e.g. on a filter lane), but for a cyclist it really isn't worth betting my life that they intend to turn and haven't just missed the filter sign.
As a driver my biggest bugbear with cyclists is pulling out without looking or signalling.