An Etymological Dictionary of the German Language/Windhund
Windhund, m., Windspiel, n., ‘greyhound, harrier,’ from the equiv. MidHG. wintbracke, wintspil; these compounds are tautological forms for MidHG. and OHG. wint, ‘greyhound.’ It is probably not connected with Wind, though the two words are instinctively associated. On account of the limited area of its diffusion, the prehistoric form cannot be discovered. Its kinship with Hund (Teut. hundo-, from hwundo-) is perhaps possible (Wind-, from hwindo-?); in that case the assonance with Wind must have caused the differentiation.