While I obviously cannot provide a cite, I personally have noticed the full moonrise exhibit the distortion that everyone seems to have experienced with the sunset.
Perhaps it’s because that the “full” sun rises and sets everyday, yet the “full” moon only occurs once a month (except for the proverbial blue moon), so people have more experience with the sun’s distortion. scr4 mentions that it might also be because the moon isn’t as bright. This intuitively sounds like it might be the reason, but I’d be interested in any physicists’ perspective… does the relative brightness affect the prominence of the refraction?