The cold air makes your tires contract and as a result, your tire sensors come on. However, to demonstrate this principle the following video looks at air in a balloon and how it contracts with a cold source, liquid nitrogen.
Ambient temperature affects tire pressure, and in the new world of TPMS, where the vehicle is constantly vigilant of tire pressure, these sometimes subtle changes in pressure could trigger the TPMS. For each 10° F of ambient temperature, tire pressures will change about 2%, or about 1 psi. So, as the seasons change, and as 70º F dips to 20º F, that could mean a difference of 5 psi and a TPMS warning light. Source: TPMS (Tire Pressure Monitoring Systems) Explained: Taking Temperature Into Account) amarilloautorepair.biz, Feb 11, 2015
Picture Source: aa1car.com