However, a leak *could* appear even when cold and off if:
* The leak is external to the pump itself: A leak might be coming from a hose connection to the pump, a corroded area of the pump housing, or a crack in the pump's housing. These can weep even when the engine isn't running.
* The leak is due to a failing water pump seal: While less common when cold, a severely degraded seal might still allow slow leakage.
* There's coolant pressure in the system: Even after the engine cools, there might be residual pressure in the cooling system that could force a small leak to appear.
In short: A leak while the engine is off and cold is unusual but not impossible. It strongly suggests a problem with the water pump (or related components), and should be investigated to prevent more serious damage to your engine.
