Etymology
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hoar (adj.)

Old English har "hoary, gray, venerable, old," the connecting notion being gray hair, from Proto-Germanic *haira (source also of Old Norse harr "gray-haired, old," Old Saxon, Old High German her "distinguished, noble, glorious," German hehr), from PIE *kei- (2), source of color adjectives (see hue (n.1)). German also uses the word as a title of respect, in Herr. Of frost, it is recorded in Old English, perhaps expressing the resemblance of the white feathers of frost to an old man's beard. Used as an attribute of boundary stones in Anglo-Saxon, perhaps in reference to being gray with lichens, hence its appearance in place-names.

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Definitions of hoar
1
hoar (n.)
ice crystals forming a white deposit (especially on objects outside);
Synonyms: frost / hoarfrost / rime
2
hoar (adj.)
showing characteristics of age, especially having grey or white hair; "whose beard with age is hoar"-Coleridge;
Synonyms: grey / gray / grey-haired / gray-haired / grey-headed / gray-headed / grizzly / hoary / white-haired
From wordnet.princeton.edu