As the following screenshots illustrate, the vegetation in vanilla 1st person "hardcore" mode, doesn't get illumated whatsoever by the moonlight, whilst buildings are. My understanding is, that there are 2 serverside settings for nighttime, "bright night" and "dark night".
I also understand that the "dark night" setting is enabled on official 1st person only servers. The reported issue does however not occurr on the "bright night" setting.
Thus I conclude it is possible for the vegetation to be illuminated.
My suggestion is, to tweak the lighting slightly so vegetation does catch light. Of course not as much as in "bright night" setting. And if the sky is cloudy then it should be as dark as it is right now.
However the screenshots were taken on clear sky, which is why the buildings are illuminated by moonlight.