Breathing in cold air is not bad for your lungs.
However breathing in cold air makes it harder for you to breathe properly and you get more tired and out of breathe.
In extreme cold temperatures those extreme cold temperatures can make it really hard to breathe so when you're out in cold air make sure to wear a scarf or something over your mouth to keep your mouth and lungs warm.
The warmer air is better for your lungs than the cold air.
Breathing cold air can make your lungs hurt and could cause you to collapse especially when you're running etc.
But the cold air itself is not gonna do any permanent damage to your lungs.