Just like when you first started running, you'll have to build up slowly to get adapted to running in the cold. The air is typically dryer so your lungs and nostrils will burn if you do too much at one go.
Another important thing is warming up adequately before starting to run. A couple sets of body weight squats, gentle shoulder rotations and neck stretches should be enough to at least get a slow jog going without you pulling or straining anything.
1) eat real food - more vegetables, moderate meat, moderate fruits, less grains, less sugar, less vegetable oils.
2) exercise - moderate intensity cardio, sprinting, heavy lifting, dedicated stretching and mobility.
3) live - relax, de-stress, meditate.
Disclaimer: I'm not professionally qualified to make any formal recommendations. I've just done my homework and I'm my own guinea pig. All of my data, unless otherwise cited, comes from a sample size of n=1 (me).