Tire pressure systems, which originally monitored tire pressure in aircraft landing gear, later evolved to alert automobile drivers of low tire pressure; all newer vehicles now require them. The system may alert you when it becomes cold for several possible reasons.
Air contracts when it cools, so cold air creates low pressure in the tires. In severe cold, when the vehicle has sat for awhile, this cold air can even cause tires to seem flat. As weather cools, monitor and correct tire pressure frequently.
The cold also makes the air less dense. Therefore, it can slip through loose valve stems that can hold denser air. Check the valve stem for tightness when monitoring tire pressure, which may allow you to correct a low tire pressure warning.
Some icy parking areas may cause a sudden drop in air pressure, causing your monitor to go off. Often manifested as a false low pressure reading, it will correct itself quickly once driving resumes. If it does not, check and correct low tire pressure immediately.