Hi Jason,
As the Earth passed between you and the Sun it would get very dark, darker than on Earth during a solar eclipse. The Earth as seen from the Moon is almost four times larger than the Moon as seen from Earth so it would cover the Sun even more completely. Maybe you could still see some of the Sun's faint corona, way out far from the Sun. I am not sure.
It would indeed get very cold. Because the Moon has no atmosphere, heating of objects on the Moon comes from being directly heated by the Sun's light - if the Sun rotates over the limb or is blocked out as it would be during an eclipse the temperature plunges.
Terry