Summary
Bumfuck, Egypt is first documented in army slang from 1972, and BFE is from at least 1988. Bumfuck, [Egypt] appears to be the original, followed by variations Bumblefuck (1989), Bubblefuck (1993) and Buttfuck (1999).
Sometimes these variations appear standing alone, sometimes in Egypt, or Africa (also found in BFA), or another country, (rural) state or place, and sometimes prefixed by East or West. More recently, both BFN and Butt Fucking Nowhere are reported from 2002.
As Bumfuck, Egypt appears to be originally military slang, given the number of abbreviations they used I can easily believe it was also jocularly and euphemistically shortened to BFA before 1988.
Partridge
The Concise New Partridge Dictionary of Slang and Uncoventional English (2003):
BFE noun any remote location. An abbreviation of BUMFUCK, EGYPT US 1989
Bumblefuck noun any remote, small town US 1989
Bumfuck, Egypt noun a mythical town that is the epitome of remoteness. With variants US 1972
It also gives BFN and Butt Fucking Nowhere, both from 2002.
OUP
These 1989 and 1972 first citations are given with others in The F-Word (2009, Oxford University Press):
BFE noun [Bumfuck (or Bumbfuck), Egypt]
Military & Students. a very remote place; the middle of nowhere.
1989 P. Munro U.C.L.A. Slang 20: Troy...lives out in B.F.E....Bum Fuck, Egypt.
Bumfuck noun
Military & Students. a very remote place. --used with a placename, esp. in Bumfuck, Egypt. Also Bumfuckistan. Jocular. See also BFE, BUMBLEFUCK.
1972 Sgt. E-6, U.S. Army: They probably sent those records out to Bumfuck, Egypt.
It also gives Bumblefuck as a 1989 alteration of Bumfuck; Bubblefuck as a 1993 alteration of Bumblefuck; and Buttfuck, usually used with a placename, from 1999.
Usenet
I found an earlier example for the initials BFE in Usenet, on 11th September 1988 in alt.cyberpunk:
$600 is about what we paid for my first computer -- a C64, 1541 and printer; when I was a upper-lower class kid living in the backwoods of
BFE, Leesville, Louisiana. (Ft. Polk sux too. :-). We weren't on
welfare, but we weren't rich either. I think we saved about 9-12months
for the computer. (Grandparents bought me a monitor a month later. What
a rescue. :-). That computer made the difference between me being
a dual major CompSci/Journalism student in Houston instead of being
like my cousins: 2-4 kids, HS diploma at best, slow paying job, no future,
and living in BFE, Louisiana.
Early on that word of course was used to talk about the action of cleaning something off with a garden hose, but that is not the meaning you are asking about. I do not recall ever hearing that term used with that meaning before the 80's. What happened in the 80's?
Well, SCTV had a very funny (to us USAsians) skit with a couple of stereotypical Canadians called the McKenzie Brothers. They were constantly calling each other "hosers", and talking about how they had "hosed" each other. The skit went the 80's equivalent of viral, with an album (with a couple of singles that got good airplay) and a movie spun off it. The effect was that we (in the USA) got "hoser" added to the language as sort of a good-natured insult, or a way to make fun of Canadian speech.
Along with it, we borrowed the verb and adverb forms of "hosed" from the same source. Its a much more useful word, so it kinda lost its association with Canadians, and got fully adopted into the USA lexicon.
So where did Canadians come up with these words? That's where personal experience fails me, so I have to rely on online sources:
Like the very similar term hosehead, the term may have referred to
farmers of the Canadian prairies, who would siphon gas from farming
vehicles with a hose during the Great Depression of the
1930s.[citation needed] The expression has since been converted to the
verb 'to hose' as in to trick, deceive, or steal - for example: "That
card-shark sure hosed me." Hosed has an additional meaning of becoming
drunk - for example: "Let's go out and get hosed." Another possible
origin is derived from hockey slang. Before ice resurfacers, the
losing team in a hockey game would have to hose down the rink after a
game. Thus the term "hoser" being synonymous with "loser".
Personally I prefer the hockey explanation, but that doesn't make it right.
Currently the OED says there is no clear evidence of the term being used prior to its use by Rick Moranis and Dave Thomas, which to my mind leaves a strong possibility that they may have invented the slang themselves (although they are both Canadian, so they could well just be the first to record an existing slang).
Best Answer
It is clear that Old English grimm is cognate with Ger grimm(ig); Koebler Althochdeutscheswörterbuch) refers this to Pokorny (Indo-European Etymological Dictionary) 458, where it is derived from PIE root *ghrem-2, “heavy sound, thunder, grumble”.
However, Koebler also notes a similar word, grimo, “helmet, mask”, which I imagine is what your informant who suggested “hooded” was referring to; it’s cognate with OE and Icelandic grima, from which Tolkien took the name of the evil counsellor Grima Wormtongue. Pokorny 457 derives these from PIE root *ghrēi-, *ghrəi-, *ghrī-, *ghrei-, “smear”, from which he also derives Middle Low German grimet, “black-streaked”, and grēme “smut”, which appear to be cognate with English grime.
Both roots were used in mediaeval personal names. Genealogical sites derive the modern surname variously from both; but they do not cite authorities and may safely be ignored.
Unless an authority can be found which definitively traces the Brothers' surname, I think the verdict must be Not Proven.