The explanation for this illusion is still not known. It is not an atmospheric phenomenon, and the Moon really does seem to be twice as large on the horizon as when it is high up in the sky, particularly in September during the Harvest Moon. The Moon obviously does not change its apparent size since if you held a penny at arms length it would cover the Moon equally well on the horizon and high over head. There must be an eye-brain basis for this effect, just as there are many other optical illusions that also 'fool' the eye.
The Moon Illusion was first mentioned in a cuneiform inscription on a clay tablet from the royal library at Nineveh in the 7th century BC. Ptolemy, ca 150 AD, tried to explain it by saying that near the horizon the eye has other things to use as a reference for judging the size of the moon. This is the 'classic' explanation that everyone seems to use. George Berkeley, in 1709, published a completely different explanation that had to do with the low Moon being fainter because of the increased atmospheric extinction which seemed to make it more distant and therefore oversized. In 1959, H. Leibowitz and T. Hartman at the University of Wisconsin proposed that it had to do with the fact that the eye-brain system is designed to work on the horizontal plane, not the vertical plane. On the horizon we process the Moon image in the optimal orientation giving us its true apparent size. Tipping our head back to view the high Moon, we see a non-optimal image. The illusion is not that the horizon Moon is large, but that the high Moon is smaller in size that it 'ought' to be.
In 1989, an entire book was dedicated to this phenomenon and edited by Prof. Maurice Hershenson at Brandeis University. The Moon Illusion Lawrence Erlbaum Associates, Publishing; Hillsdale New Jersey. By 1985 there were at least 8 explanations for this illusion in the literature with little consensus over a true explanation. The bottom line is that the Moon Illusion is so deeply coupled to the general problem of human space perception that the experts do not as yet understand all of the physiological factors that contribute to it. The conclusion of the book is that we have to first agree on the cognitive aspects of how the brain and the visual cortex extract spatial information, and then somewhere in all of that will lie the explanation for the Moon Illusion.