Temp-related issues. When its cold out, muscles tend to be tighter and stretching is especially important. It takes longer to warm up, but its important to do to avoid injury. Cold air can precipitate asthma and reactive airway disease, so keep your neck warm. When its over 65 degrees our bodies have a harder time not overheating. When its warm stay hydrated, drink plenty of cold fluids, and wear loose clothing.
Layers, footing. You may have to wear layers, better footing aids, and be aware of temps.
Running. Additionally , in the winter you need to warm the air entering the lungs with mouth breathing as the cold air can crystallize in the alveoli leading to pain. Also there are slip and fall hazards with winter running in cold climates. So - dress warm , cover your mouth to warm the air going to your lungs and be careful where and when you run .