Why doesn't the moisture freeze out of the air when the air temperature is below freezing? I would think that there would be zero humidity outside right now and it's 21 degrees. The weather site says there is 71% humidity.
 A: Even at the height of summer, it's well below the boiling point of water, and yet there's still water vapor in the air. The reason that water vapor can exist in the atmosphere below the boiling point is the same reason that water vapor can exist in the atmosphere below the freezing point. Water can exist in vapor form even at very low temperatures.
If you have a modern refrigerator/freezer, you've probably seen ice cubes that have become smaller and riddled with holes when left in the freezer for a long time. This is because your freezer operates at an extremely low humidity to keep ice from depositing on the walls of the freezer. This low relative humidity makes the cubes gradually sublimate (transform directly from ice to water vapor without passing through the liquid state), resulting in a decrease in size and a pockmarked surface.


I would think that there would be zero humidity outside right now and it's 21 degrees.

The answer to your question is found in the phase diagram for water, depicted below.

Source: https://en.wikipedia.org/wiki/File:Phase_diagram_of_water.svg
Note that water vapor, marked in tan in the above diagram, exists well below freezing. Below the triple point, ice sublimates directly into water vapor without transitioning to liquid water. (Similarly, water vapor at temperatures below the triple point temperature undergoes deposition to directly transition from vapor to ice, without an intermediate transition to liquid water.)
The reason water can exist in vapor form below the boiling point is that atmospheric pressure is irrelevant. All that matters is the partial pressure of the water vapor in the air. Liquid water will evaporate and ice will sublimate when the partial pressure is below the saturation level. The partial pressure of completely saturated air can be found as the point at which a vertical temperature line intersects the upper boundary of the tan region in the above phase transition diagram.


The weather site says there is 71% humidity.

Relative humidity is the ratio of the amount of water vapor that is present in the air versus the amount of water vapor that would be present in completely saturated air at the same temperature. The saturation pressure at -6° C (21° F) is 364 pascals. That represents about 3 grams of water vapor for every cubic meter of air. 71% humidity means that the air instead held about 2 grams of water per cubic meter.
A: Also water in the form of ice has a temperature dependent vapor pressure. See this graph in Wikipedia. Therefore, at temperatures below freezing (0˚C), the vapor pressure is lower than above freezing but not zero.
A: The same reason streams don't freeze until quite low temperatures: the air is moving. In order for ice crystals to form, the water molecules have to align just right. They also have to be moving slowly enough that when they come together they don't just bounce of each other.
On the other hand, water molecules can latch onto solid things like dirt or houses, which is why you might get frost. But again, this only happens if the air is calm enough.
