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There is no fixed air temperature for frosty breath. As meteorologist Tom Skilling explains, two factors determine whether we can see our breath in cold weather: temperature and humidity. Exhaled air has relatively high amounts of moisture from our lungs. When this warm, moist air is chilled, the moisture condenses. The exhaled air is chilled below its saturation temperature, or dew point. For big dramatic clouds of frosty breath, it helps to have humid air. Why? This stops the condensation cloud from evaporating too quickly. The water droplets will last longer in moist air, because the air is already fairly saturated.
Here's a nifty piece of frosty breath movie trivia, courtesy of IMDb. The outdoor shots in "Dog Day Afternoon" were filmed during the winter, but the story was supposed to take place during the summer. So to make their breath less visible, the actors held ice in their mouths before filming.
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