I've worked out a little in the cold before. Definitely pay a little more attention to the warm up, for sure. But once you're warmed up everything should be the same. For the cold air, I think it helps to try to inhale through your nose as much as possible. That allows the air to warm up at least a little bit before it gets to your lungs. Also, remember to stay hydrated. You won't sweat as much as in warm weather, so it's easy to forget.
Anyway, that's what I've done in the past. You may want to Google on it a little for more "expert" advice.