On your body
Start with some barrier cream/gel (like petroleum jelly) on sensitive areas to prevent chaffing and wind-burn. If you’ve never experienced either of these things, lucky you!
Then wear a long-sleeved base layer next to your skin, preferably in a wicking-fabric which will take the sweat away.
If you feel the cold, the wind-chill looks like it will be a factor or you’re doing some interval training with long gaps between efforts, a warm layer, like a fleece is advisable.
Finally, top it off with something windproof (if it’s going to be wet, something waterproof and wind-proof will be best).
You should really be training in long leggings when it’s cold, too; a little extra warmth will create more capillaries and so increase blood-flow to your muscles.
Hats and gloves are also recommended, but take care not to let yourself overheat; if you start to feel dizzy or lightheaded, please stop!
Always wear something bright/reflective when you’re training in public spaces and remember that COVID-distancing is more important than your run.
At the time of writing, we’re still being asked to stay away from people with whom we do not live. Try to find a route with minimal traffic, to allow you into the road if necessary, and wide footpaths.
In terms of avoiding icy patches, try pavements which are beside bus-routes. These roads are often gritted, which means the pavements usually are, too.
Alternatively, find some grass to train on. Test out any surface carefully before you run on it in earnest; IF IN DOUBT TURN DOWN THE PACE!