When the water vapor in the air reaches saturation, will it make the air rise and the temperature drop, or will it be easier to produce precipitation after the cold current cools the air? Why?

When a cold front crosses the border, it usually appears cloudy, windy, rainy (snowy) and cool. After the cold front crossed the border, the cold air mass occupied the position of the original warm air mass, and the temperature dropped, the humidity dropped, the air pressure rose, and the weather turned fine. When the warm front crosses the border, the clouds become thicker and cover the sky, often forming continuous precipitation (that is, long-term continuous precipitation). After the warm front crossed the border, the weather was controlled by the warm air mass, and the temperature increased, the humidity increased, the air pressure decreased, and the weather turned fine.

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