Warm air rises and cold air sinks due to the basic laws of thermodynamics. When air gets warmer, the molecules of that air gain energy and move faster around each other. This makes the molecules of that air farther apart from each other, which decreases their density. Because colder air has a higher density than warm air, it is heavier and will sink. This is why you can see a natural phenomenon such as this experiment in your own kitchen.

When the warm air from the hot water gets nearer to the bottom of the container, the blue and red water remain seperated because the cold water is more dense than the warm water. This is the same principle that makes thunderstorms work. When the warmer air gets close to the surface of the Earth, it becomes less dense and forms a thunderstorm. The same is true when the cold air gets close to the ground. When the cold air becomes denser, it is heavier and sinks, forming another storm.

This is why cold air tends to stay closer to the ground than warm air. It is also why it is cooler at high elevations like mountaintops, as the air is further from the sun and closer to the ground.

This is why it can be difficult to breathe in cold weather for people with asthma and other respiratory conditions. The dryness of cold air can thicken mucus in your lungs, making it harder to breathe and causing flare-ups. Cold temperatures also lead to more indoor time, which means more exposure to indoor allergens and irritants such as dust mites, mold spores, pet dander, smoke from cigarettes, and barometric pressure changes.