The air you breathe out is warm and moist.
It contains water vapor from your lungs and airways.
Most of the time, that moisture stays invisible.
Cold weather changes the situation.
Your warm breath cools quickly
As you exhale, the warm air mixes with much colder surrounding air.
Its temperature drops.
Cooler air cannot keep as much water in invisible vapor form under the same conditions.
Tiny droplets begin to form
If the exhaled air cools enough, some water vapor condenses into countless tiny liquid droplets.
In very cold conditions, tiny ice particles may form too.
Those particles scatter light.
That is what makes the little cloud visible.
It is similar to fog
The process is closely related to how fog forms.
Fog is also made of tiny suspended water droplets created when moist air cools enough for condensation.
The main difference is that visible breath happens in a small moving cloud right in front of your face.
Are you breathing out more water in winter?
Not simply because you can see it.
You exhale moisture in warm weather too.
The difference is what happens after that moisture leaves your body.
On a warm day, it usually remains invisible as it mixes into the surrounding air.
Why does the cloud disappear so quickly?
The droplets spread into a larger amount of surrounding air.
They may evaporate again as conditions change.
The tiny concentrated cloud becomes too diffuse to see.
Is visible breath smoke?
No.
It may look smoky, but the visible material is mostly condensed water droplets and sometimes tiny ice particles.
So you are always breathing out moisture.
Cold air simply makes some of it visible for a few seconds.
And that’s the short explanation.
Related explanations: Why does fog form?, Why do clouds stay in the sky?, and Why does glass fog up?