Wear gloves, mittens and good socks. I prefer mittens because they allow me to keep my fingers together. Protect exposed skin and lips with petroleum jelly. Or wear a balaclava. Take it easy on slippery surfaces.
Some people love running on a soft snowy surface.
Watch out for ice. Take extra time to warm-up. The colder the temperature, the longer it takes to raise your body temperature. A winter warm-up should last a minimum of 8 minutes or until you're sweating slightly. Cold weather causes tightness in connective tissue and muscles fibres, making it harder to limber up.