Your question got me curious, so I tried googling. I didn't come up with much past the "carbon during the day/ oxygen at night" plant biology basics, but I did find this from Cambridge University:
http://www.thenakedscientists.com/HTML/questions/question/1769/ . The part I found most interesting was this:
"I’m sure many of you are familiar with the folding of leaves that we see in the clover growing in your lawns and lots of plants in the garden fold up their leaves at night. Darwin was interested in this and thought that it was to do with the leaves trying to maintain their heat balance at night. What we think is happening now is that the leaves are trying to avoid moonlight so as to prevent their circadian rhythms being disrupted by those very light intensities because they certainly do respond to moonlight."
It kind of makes me wonder how much old agricultural lore about planting, cultivating, and harvesting during certain moon phases might be from generations of growers observing changes in the plant triggered by moon cycles. I'd really love to see if there's any correlation between when plants begin to flower or when fruit ripens with the phase of the moon (and how it might be affected by day length, and if that contributes to a good year or a bad year for certain crops).