When we breathe out, carbon dioxide rich air from our lungs is let out. The process of respiration uses oxygen from the air we breathe in and adds carbon dioxide to the air we breathe out. This also leads to the addition of water vapor in the air that is exhaled.
This water vapor in the exhaled air condenses when we breathe out on a cold day, and the mist like appearance of the condensed water vapor is colloquially described as “see your breath." It is only the water vapor in our breath that is condensing to form micro particles of water that is visible, not the other gases which include nitrogen, carbon dioxide and oxygen.