What would the moon look like to someone at the South Pole? To a first approximation, it's bisected by the horizon. But how far above and below does it get?
The moon orbits close to the plane of the ecliptic, which is tilted at 23.5 degrees to the equator, the moon is slightly off the ecliptic, and can be about 5 degrees above the ecliptic.
So, on the winter solstice (June 21) if full moon happens to be furthest from crossing the ecliptic, the moon would be 28.5 degrees above the horizon: roughly a third of the way between the horizon and the zenith. It can get the same distance below the horizon, and during summer the full moon would not be seen at all.
Our moon is unique in being close to the plane of the ecliptic, and not in the plane of the equator, which suggests its formation was not like that of other moons in the solar system.