The Moon isn't actually any larger on the horizon, it just appears larger. This phenomenon is known as the "Moon illusion" and is more pronounced at around full Moon when the maximum area of its disc is illuminated. The moon illusion has been known since the Aristotle first documented the illusion in the 4th century BC.
In reality, the Moon has more or less the same apparent diameter of around half a degree, whether it is looming over the horizon or riding high in the sky. One explanation for the Moon illusion arises from our perception of the shape of the celestial sphere above us; instead of a hemisphere, we perceive the sky to be shaped like a flattened dome. Consequently, the lower the Moon is in the sky, the further away and larger it is perceived to be; when the Moon is high in the sky we perceive it to be closer to us and therefore smaller in apparent size.
Few people seem to be immune to the Moon illusion, even though the viewer may be fully aware that for any given evening there is actually no appreciable difference in the Moon's apparent diameter, regardless of its height above the horizon.