Pressure changes more rapidly with height in air that is more dense.
At a given pressure, air that is colder is more dense. Putting it together, for two columns of the same height, the denser column will have the larger change in pressure from top to bottom. Similarly, for two columns spanning the same pressure interval, the denser column will be shorter. I don't want you to come away with a common misconception. It's easy to skim through all this and think that cold temperatures correspond to high pressures.