You could die from running in too cold of weather especially if the cold weather is below freezing.
You use more energy to stay warm when you're running in the cold which could cause over exertion and lead to a heart attack or you could also develop hypothermia which can cause you to die.
Running in cold weather though is pretty safe as long as you dress appropriately, wear gloves and not stay out running for more than 30 minutes at a time without going inside somewhere to warm up.