The moon looks larger when it is closer to the horizon because you see it in reference to familiar object like buildings, trees and people.
As the moon rises it is farther from the objects that provide a frame of reference. When you observe the moon in the wide, vast sky it only looks smaller.
If you hold your thumb or forefinger at arms length and close one eye you can measure the width of the moon. Try this at dusk and again a few hours later and you will see the moon stays the same size.