That is not true.
Hot water can cool down faster because of the higher difference in temperature.
But by getting cooler the temperature difference decreases and therefore the cooling rate, too.
E.g.: Water at boiling point = 100°C in surroundings of freezing point = 0°C cools down faster from 100°C to 50°C than 50°C to 0°C.
But it still has to take the same time from 50°C to 0°C once it reaches 50°C.
So water from 50°C to 0°C takes X minutes while water from 100°C to 0°C takes X+Y minutes.
It does NOT cool faster to 0° than the 50°C water.