The association of hares, rabbit with moon deities leapt through myths, legends, and folk tales all around the world.
Many cultures, when looking at the moon, see the outline of a hare or rabbit, who lives on the moon. A great example being the mid-autumn festival.
They are often seen as an intermediary between the lunar deities and humans. 
From the Chinese, Aztec, Celt to the Egyptian, the association of hares, rabbit with moon deities leapt through myths, legends, and folk tales all around the world. 
Sweet and innocent or trickster in nature? You decide.