According to the website ScienceBits, the reason breath is visible in cold weather is due to the condensation created when warm, humid air from the lungs collides with the colder, outside air Because frigid air cannot hold as much water vapor as hot air, the resulting saturation of water vapors into the atmosphere becomes visible to the human eye.
The water droplets and tiny ice crystals that form from breath expelled into cold air can be likened to the formation of fog and clouds. According to the website Wonderopolis, the reason breath isn't visible in warm temperatures is because the water vapors can remain in an invisible gas form. Warm air provides energy for molecules to move around freely and remain in gas form while cold air causes molecules to bunch up, slow down and change into a liquid or solid state.
While there is no specific temperature in which breath can be guaranteed to be visible, 45 F and below is the typical tipping point. Additionally, the greater the relative humidity, the greater the chance of seeing breath in cold air. This means that in high humidity, when the air is already filled with moisture, the thermometer doesn't have to read quite as cold to see breath in the air.