Your description of a cold front is accurate! To elaborate a bit more:
A cold front occurs when a cold air mass moves into an area occupied by warmer air, causing the warmer air to be displaced upward. This can lead to various weather phenomena, including the development of clouds, precipitation, and often stormy weather as the warm air cools rapidly. Commonly, the approach of a cold front is marked by a drop in temperature, changes in wind direction, and the possibility of thunderstorms or heavy rain.
After the cold front passes, the weather typically clears up, often resulting in cooler, drier, and more stable conditions. Overcast and cloudy days can persist for some time afterward, depending on other atmospheric conditions.
If you have more questions about weather phenomena or related topics, feel free to ask!