Do celestial bodies actually appear larger along the horizon? Whether it be the moon (especially when full) or tonight, as Mars is closer than it has been in decades, it appears that these bodies are larger when close to the horizon than overhead.

Is this an optical illusion (i.e. the actual appearance is no larger), or is there some refraction or other effect that actually makes the appearance larger?
No, it's an illusion. Probably the ancient one. Simple experiment you can do is, set grid on telescope, measure the angle subtended when moon is at horizon and when moon is atop. You will see angle subtended by moon is same, hence the size are same. It's merely an illusion.

For more details:
https://en.m.wikipedia.org/wiki/Moon_illusion