Why Can Breath Cool Hot Soup Yet Warm Cold Hands?

Blowing across hot soup makes it cool faster, yet breathing gently onto your hands in winter can warm them. The difference is not that exhaled air suddenly changes from cold to hot. The direction and rate of heat transfer change with the object and with how the air is delivered.

Above hot soup is a thin layer of warm, humid air. A continuing airflow removes that layer and replaces it with cooler, drier room air, increasing convection and evaporation. Evaporation requires energy, which is drawn from the soup, so cooling speeds up. A narrow, fast jet from pursed lips also entrains surrounding air; under ordinary conditions, its cooling effect is not mainly caused by the air expanding.

Cold hands reverse the situation. Air breathed slowly through an open mouth is usually warmer than chilled skin and contains substantial water vapour. It can transfer heat to the hands by convection, and condensation on a very cold surface also releases energy. If you blow forcefully through pursed lips from farther away, the breath mixes with cool room air and increases evaporation from the skin, so it may feel cool instead.

It is therefore too simple to say that wind is cold or breath is hot. Moving air changes the rate of exchange. Whether something warms or cools depends on temperature difference, humidity, distance, speed and whether the surface is wet.

https://openstax.org/books/university-physics-volume-2/pages/1-6-mechanisms-of-heat-transfer
https://openstax.org/books/physics/pages/11-3-phase-change-and-latent-heat