The puzzle assumes that the room temperature is greater than the cold milk's temperature. When I added that the room temperature is, say, -10 °C, Mercury fails to see the difference.
Under any reasonable assumptions for the size and shape of the cup, the amount of coffee, the makeup of the air, etc., the room being -10c won't change the result.
It would only matter if the air were able to cool the coffee to a temperature less than that of the milk in under 2 minutes.
The puzzle assumes that the room temperature is greater than the cold milk's temperature. When I added that the room temperature is, say, -10 °C, Mercury fails to see the difference.