Is an oxygen/nitrogen cycle possible, given a cold enough climate?

Suppose for whatever reason the sun's power has weakened. The Earth gets colder. All the water has frozen, and the temperature is getting to around the boiling point of oxygen.

Can an "oxygen cycle" be possible, in which oxygen reaches it's boiling point and begins raining, forming lakes, evaporating, and forming clouds, like the water cycle today? Where perhaps in the summer, oxygen rains, and in the winter, nitrogen/oxygen and other trace gases rain and maybe in the polar regions, the atmosphere itself starts snowing?

Would this be possible, or is the changing air pressure, temperatures and properties of the gases prevent that kind of phenomenon from happening?

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Is an oxygen/nitrogen cycle possible, given a cold enough climate?

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