The Moon Illusion has been studied for centuries. It was first mentioned in a cuneiform inscription on a clay tablet from the royal library at Nineveh in the 7th century BC. Although the moon's image does not change size, the moon seems to be twice as large when it is seen on the horizon compared to when it is viewed overhead. You can verify that it's retinal image never varies. Hold a dime at arms length and it would cover the moon equally well whether it's on the horizon or over head. Ptolemy, ca 150 AD, theorized that near the horizon there are objects to use as a reference for judging the size of the moon, and differences in judging the moon's distance give rise to the illusion. Berkeley (1709) argued that the low moon was fainter because of the increased atmospheric extinction which made it seem more distant and therefore oversized. Others have 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 (Leibowitz & Hartman, 1959). 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 over head moon is smaller in size than it 'ought' to be.
Others have argued that comparisons with buildings and other objects on the horizon vs none above are
responsible for the differences between the moon's apparent size when looking horizontally and looking vertically (this explanation is contradicted by the fact that the Moon Illusion also occurs over open water).
Contrary to most observers "seeing" the horizon moon as being closer, it may actually be judged to be farther away when it is on the horizon versus at its zenith, leading to a corresponding mistake in our perception of its size.
An overview of the phenomenon is available in a book (M. Hershenson (Ed.), The Moon Illusion, Erlbaum: Hillsdale, N.J., 1989 ) and in a detailed presentation on the WEB.