Once hyphenated and twice not?  This apparent contradiction arouses my curiosity!

• 06.067 down the hillsides from their gate
• 06.086 and there with the light of the moon on a hill-side rock or a stream
• 09.018 from the hillside there was a water-gate.

To my surprise, the hypenated or two-word form are attested in OED, the single-word form is not… until it is itself one member of a combination word

1890   Daily News 20 Dec. 5/6   The name ‘Hillside men’..applied to the Fenians.

“hill-side, n.” OED Online, Oxford University Press, June 2017, http://www.oed.com/view/Entry/87009. Accessed 14 September 2017.