When you start a cold engine, especially in cold weather, a thermostat valve is closed, thus the coolant flows in a small circle bypassing the radiator. This helps the engine to reach its operating temperature faster. This explains why the lower hose is cold – heated coolant doesn’t flow through it.
As soon as the engine reaches its operating temperature, the thermostat valve opens fully or partially. Hot coolant flows through the radiator, and the lower pipe should become warm. If this doesn’t happen, your car may have the following problems:
clogged hoses;
airlocks in the hoses;
water pump failure;
stuck thermostat.
Visit a car service station for thorough diagnostics.