It is funny to find this site my husband and I were wondering the origin of Mr. Moon and thought we'd look it up on the net but it seems no one else knows anything either here's is what we grew up hearing in southern Ohio:
Mr. moon, moon bright and shiny moon
hiding behind the trees
here comes the farmer with his big shot gun
he's goin' get ya if you start to run
oh Mr. moon, moon bright and shiny moon
won't ya please shine down on, please shine
down on, please shine down on meeeeeee.
I guess I thought it had something to do with a slave trying to run away and needing the moonlight so I had guessed it to be an old slave song?