deerskin (n.)

Old English deor "wild animal, beast, any wild quadruped," in early Middle English also used of ants and fish, from Proto-Germanic *deuzam, the general Germanic word for "animal" (as opposed to man), but often restricted to "wild animal" (source also of Old Frisian diar, Dutch dier, Old Norse dyr, Old High German tior, German Tier "animal," Gothic dius "wild animal," also see reindeer).

This is perhaps from PIE *dheusom "creature that breathes," from root *dheu- (1) "cloud, breath" (source also of Lithuanian dusti "gasp," dvėsti "gasp, perish;" Old Church Slavonic dychati "breathe"). For possible prehistoric sense development, compare Latin animal from anima "breath").

The sense specialization to a specific animal began in Old English (the usual Old English word for what we now call a deer was heorot; see hart), was common by 15c., and is now complete. It happened probably via hunting, deer being the favorite animal of the chase (compare Sanskrit mrga- "wild animal," used especially for "deer"). 

Deer-lick "salty spot where deer come to lick," is attested by 1778, in an American context. The deer-mouse (1840) is so called for its agility.

c. 1200, "animal hide" (usually dressed and tanned), from Old Norse skinn "animal hide, fur," from Proto-Germanic *skinth- (source also of Old English scinn (rare), Old High German scinten, German schinden "to flay, skin;" German dialectal schind "skin of a fruit," Flemish schinde "bark"), from PIE *sken- "to peel off, flay" (source also of Breton scant "scale of a fish," Irish scainim "I tear, I burst"), extended form of root *sek- "to cut."

Ful of fleissche Y was to fele, Now ... Me is lefte But skyn & boon. [hymn, c. 1430]

The usual Anglo-Saxon word is hide (n.1). Meaning "epidermis of a living animal or person" is attested from early 14c.; extended to fruits, vegetables, etc. late 14c. Jazz slang sense of "drum" is from 1927. Meaning "a skinhead" is from 1970. As an adjective, it formerly had a slang sense of "cheating" (1868); sense of "pornographic" is attested from 1968. Skin deep is first attested in this:

All the carnall beauty of my wife, Is but skin-deep. [Sir Thomas Overbury, "A Wife," 1613; the poem was a main motive for his murder]

The skin of one's teeth as the narrowest of margins is attested from 1550s in the Geneva Bible literal translation of the Hebrew text in Job xix.20. To get under (someone's) skin "annoy" is from 1896. Skin-graft is from 1871. Skin merchant "recruiting officer" is from 1792.