Yes, according to fundamental gas laws, when a given mass of air gets colder, its density increases and its pressure drops if volume is restricted, but in the context of the Earth's atmosphere, cold air is actually denser and heavier than warm air, leading to higher surface barometric pressure. As air cools, molecules lose kinetic energy, slow down, move closer together, and contract, causing the air column to shrink and become heavier, which creates a high-pressure system at the surface. Conversely, when air warms up, it expands, becomes lighter and less dense, rises, and creates a low-pressure area near the ground. You can monitor local barometric changes using a digital barometer. You can verify these meteorological principles when observing how passing cold fronts consistently bring rising surface air pressure and clear skies.
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