Latent heating/cooling is contributing toward a phase change. Sensible heating/cooling can be sensed, because it changes temperature.
If I have a bowl of ice and water at equilibrium, and slowly add heat, the temperature doesn’t change, but the ice will gradually change phases to liquid water. After all the ice is melted, the temperature will go up.
When you feel cool air, it’s sensible (consider that you sensed it). There’s no phase change.
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