When we breathe in cold air the cold air rushes into our warm lungs and when that cold air hits our warm lungs it causes spasms in our lungs.
Those spasms in our lungs due to the cold air hitting the warm air in our lungs is what makes it harder to breathe when it's cold out.
A good idea is to wear a scarf over your mouth to protect your lungs from the cold air which will make it easier for you to breathe especially if you're outside running in the cold or are doing any straining activities.