Is it farther or further?
"thick, obscuring mist," 1540s, probably from a Scandinavian source akin to Danish fog "spray, shower, snowdrift," Old Norse fok "snow flurry," fjuk "snow storm." Cf. also Old English fuht, Dutch vocht, German Feucht "moist." Figurative phrase in a fog "at a loss what to do" first recorded c.1600.
"long grass," c.1300, probably of Scandinavian origin, cf. Norwegian fogg "long grass in a moist hollow," Icelandic fuki "rotten sea grass." The connection to fog (n.1), via a notion of long grass growing in moist dells of northern Europe, is tempting but not proven. Watkins suggests derivation from PIE *pu- "to rot, decay."
1590s, from fog (n.1). Related: Fogged; fogging.
[origin unknown; probably a substitution for smoke in all senses]