Why does the moon appear larger close to the horizon?
Larger near the Horizon, Smaller Overhead
The constellations and the Sun and the Moon seem to be larger when they are close to the horizon than when they are overhead, because your brain plays tricks on you. The constellations aren't really larger when they are close to the horizon. You can check this for yourself if you compare the size of the constellations with (for example) the size of your fist when you extend your arm fully, or if you compare the size of the Moon with the width of your thumb when you extend your arm fully. Check this when the constellation or Moon is high in the sky, and also when the constellation or Moon is low in the sky. Their size is the same in both situations.
I think that a constellation seems large near the horizon and small overhead because you unconsiously compare it to different things. When it is low in the sky, then you compare its size with that of far-away things on Earth, such as a building or mountain near the horizon, and then the constellation or Moon seems to be quite large by comparison. When it is overhead, then you see the Moon or constellation in the middle of an even much bigger sky, and then it seems small by comparison.
Try to estimate how large (in inches or centimeters or feet or meters or kilometers or miles) the Moon is when it is close to the horizon and when it is high in the sky. I expect that the answer is smaller when the Moon is high in the sky than when the Moon is near the horizon.
I did not mention refraction in the explanation I just gave. Refraction lifts up the image of a celestial object near the horizon, and the more the closer the object is to the horizon. Refraction can only have a systematic effect in the vertical direction, because the atmosphere is layered only in the vertical direction. It is impossible to make everything appear, for example, twice as large in the horizontal direction, because if that happened everywhere along the horizon, then the horizon would have to be twice as large in circumference, and that doesn't fit. So, the image of the Sun (the solar disk) is equally wide at every height above the horizon.
The effect of refraction in vertical direction can be seen in the Sun or Moon when they are low in the sky, because then the Sun and the Moon appear a little squashed, because the bottom is lifted up more by refraction than the top (because the bottom, as long as it is visible, is closer to the horizon than the top). The Sun appears to be 15% flatter when the bottom of the solar disk touches the horizon. When the bottom of the Sun is still 1 degree (two diameters) above the horizon, then the flattening is 10%. If the Sun is 5 degrees above the horizon, then the flattening is only 2.5%.
So, refraction close to the horizon does not make the image of the Sun or Moon larger, but rather smaller, because it is flattened in the vertical direction. The effect is at most 15%, and in the wrong direction, so it cannot explain the "small when high, large when low" effect, which works in the other direction, does not change the shape, and appears much greater than 15%.
*** I got this information from another website, so the idea/theory is not mine. ***
It is a trick played by our minds to adjust the size of the moon to compensate for the increased distance between you and the moon when it is near to the horizon.
When we focus on the moon at the horizon, we focus on the moon at a great distance. The overhead moon lacks visual cuesvthat tell us how far away the moon is, so we focus on the moon as if it was near us.
In all, the moon does not change size or shape, it is just our mind playing a trick on us, an optical illusion.