Yes. Not just the moon, but constellations as well. Maybe other things. There's no consensus on why. Refraction is one idea. Another is its the way our brains process the information from our eyes.
Brain processing shouldn't affect apparent size. Apparent size can be measured easily. I'd guess the difference in apparent size between something at zenith and on the horizon is less than a percent.
I've been getting the moon in perfect view from my kitchen window for the last several evenings. It gets great framing from the treelines on the local hills and the walls of nearby buildings. I think the framing helps you to focus on the moon (it's relatively bright compared to the rest of the scene) and appreciate the detail (some of which you can actually see with decent human vision). You are also seeing it right next to objects that you have more familiarity with their size, which helps you to appreciate the scale of the object.