An Etymological Dictionary of the German Language/Hain
Hain, m., ‘grove,’ made current by Klopstock as a poetical term. The form of the word, as is shown under Hagen (1), may be traced back to MidHG., in which, however, Hain is but a rare variant of Hagen; it signified orig. ‘thorn-bush, thorn, fence, abatis, enclosed place.’ Thus the word does not imply the idea of sacredness which Klopstock blended with it.