Refer to figure.
Colder air is denser (heavier) therefore the isobars will tend to compress one over each other approaching the ground. Therefore, the pressure falls more rapidly with increasing altitude. For instance, the 800 mb isobar indicating 6500 ft will be closer to the ground in a cold air column and will be higher in a warm air column (check the True Altitude arrows). In other words, your true altitude will be less in cold air than in warm air. This will make your altimeter to overread.