The word "mask" meaning a covering for the face entered English only in the 1530s as "maske" or similar, borrowed from Middle French masque ("a covering to hide or guard the face"). From there, it traces its way back to Italian maschera (or its variant mascara, attested from the 13th century), meaning "mask" or "disguise." This Italian term derives from Medieval Latin masca (or mascha), recorded from around the 7th–8th centuries, where it meant "mask," but also extended to "specter," "nightmare," or "evil spirit."
After that, of course, the trail goes cold. One possible "ultimate origin" is Arabic maskharah (مَسْخَرَة), meaning "buffoon," "mockery," or "object of ridicule," derived from the verb sakhira ("to ridicule" or "to mock"), which could just about tie into the idea of a mask as something used in jest, disguise, or theatrical mockery. (In classical Latin, meanwhile, the term for a theatrical mask was persona, which evolved into our word "person," but originally meant the "mask" through which an actor's voice sounded—per sonare "to sound through".)
An alternative Romance/Germanic or pre-Indo-European root might be via Provençal/Occitan mascarar ("to blacken" or "smear the face"), Catalan mascarar, or Old French mascurer ("to black the face"), which links to words for darkening or soiling the face (as a form of disguise), possibly from a root mask- meaning "black" or related to "smear/blacken." Some then connect this to a pre-Indo-European substrate in southern Europe, or even a distant link to Germanic words like English "mesh" (from Old English mæscre or Proto-Germanic maskōn, meaning "net" or "mesh"—perhaps evoking a net-like face covering).*
In any case, the word entered English and replaced older English terms like grīma (Old English for "mask," surviving in "grime") and displaced borrowings like viser (from Old French for "visor"). Meanwhile, Old Norse had gríma (“a kind of face mask”) and of course Óðinn's given name Grímr - sometimes translated "the Masked One" and sometimes "the Hooded One". We would have to reconstruct the equivalent for his Old English cognate Woden, but it's easily enough done. *Grim may well survive not just in the English surname Grim, but also in place names such as Grim's Ditch and Grim's Dyke - not to mention figures from folklore and symbolism such as the Church Grim and of course the Grim Reaper.
The Swedish word mask on the other hand means 'worm', and is cognate with the English word 'maggot', which of course ultimately comes from Old English maþa, and thither from Proto-Germanic. It's cognate with the English word 'mawk', meaning a slattern - although we also get the word 'mawkish' from it, which traditionally meant literally sickly rather than in the metaphorical modern "sentimental" sense.
And then of course we have the Latin word musca, meaning 'a fly' - and whence of course "mosquito", and so on. Jonson was perhaps having a certain amount of fun with the (somewhat recondite) wordplay in Volpone, when he has Mosca (a man whose name means 'fly' and who is literally a parasite - i.e. one who eats at another man's table) declare
"Tut, forget, sir.
The weeping of an heir should still be laughterUnder a visor."
In any case, it's a declaration that neatly sums up the cynicism of a play that is all about disguises, deception and corruption.
One wonders of course what went through Tolkien's mind when he came up with character names like Farmer Maggot and Gríma Wormtongue. He insisted that the former was just a meaningless Hobbitish name, and I suppose we have to take his word for it. (The idea of associating a humble arable farmer, working in the boggy soil of the Marish, with earthworms clearly just wouldn't do!) The latter though of course seems much more likely. (Wormtongue is a character with more than one mask!)
But deeper and further back one cannot help but think of the original grim-faced, masked warriors of Tolkien's legendarium - his dwarves, who were themselves the literary descendants of "the maggot folk of Ymir" in Gylfaginning.
It was their custom moreover to wear great masks in battle hideous to look upon; and those stood them in good stead against the dragons. For the Naugrim could withstand both fire and the wrack of battle better than any of the other speaking peoples; and it is said that the iron of their helms and their axes and their mail was so hard that the blows of the Orcs were turned aside or broken.
[The Silmarillion]At the Nirnaeth Arnoediad it was their masks that allowed the Dwarves of Belegost momentarily to the turn the tide, and even to wound and force the retreat of great worm Glaurung himself.
*Wiktionary notes "mask" (face covering) as a doublet of "mesh" in this sense. And alas there is no direct connection to unrelated words like Hebrew masekhah, which means "molten image" in biblical Hebrew and has been repurposed in modern Hebrew for "mask" partly due to phonetic similarity.