Heill Konráð!

> ON Rögnis reið is solid, but I'm not sure how old *karls vagninn is;

There might be some evidence that the 'vagn' part at least is old:
"Hvernig skal kenna himin? Svá at kalla hann ... land ... vagna
(Skáldspaparmál). In the plural because Ursa Minor was also thought
of as a wain? I guess Rögnir would be from PrN *Ragunîz, parallel to
Go. ragineis "governor", and related to ON 'regin'.

> Yes, wain=wagon; Charles' (ON Karlamagnúsar, gen.) could be a later
> confusion for *karls/carls?

'wain' is the native form inherited from Old English; wagon (sometimes
spelt waggon) was borrowed from Dutch in the 16th century.

Grimm cites a line from the Old Swedish Riming Chronicle where the
Wain is apparently related to Þórr: "Thor statt naken som ett barn,
siu stjernor i handen och Karlewagn" [
http://www.northvegr.org/lore/grimmst/022_05.php ], [
http://www.vikinganswerlady.com/stars.shtml ], but also says that "it
is Wôden stories in particular that are transferred to the Frankish
Charles." Maybe there were different ideas about who rides the
heavenly Wain in different parts of Scandinavia and the rest of
Germanic world? 'Reiðar týr' seems to be a kenning for Þórr, not
attested in the surviving poetry [
http://www.hi.is/~eybjorn/ugm/lp/r1.html ], although he's associated
with the word 'hógreið' (gentle chariot) in Haustlöng.

I always assumed that the connection with Charlemagne was a later
confusion too, but the OED comments on the English name: "The name
appears to arise out of the verbal association of the star-name
Arcturus with Arturus or Arthur, and the legendary association of
Arthur and Charlemagne; so that what was originally the wain of
Arcturus or Boötes (`Boötes' golden wain' Pope), became at length the
wain of Carl or Charlemagne. (The guess churl's or carle's wain has
been made in ignorance of the history.)"

How can they be so sure, I wonder? They might be right, but I don't
this this is really proven by the citations they give. The earliest
reference they offer which associatates it with Charlemagne, is from
1398, 'Arcturus is comynly clepid in Englis Cherlemaynes wayne'
(clepid = called).

The oldest reference given by the OED is from 1000: "Arhcton hatte an
tungol on norð dæle, se hæfð seofon steorran and is gehaten
septemtrio, þone hatað læwede menn Carleswæn." (There is a
constellation in the north that has 7 stars and is called septemtrio,
which uneducated folk call Carl's Wain.)

Richard Hinkley Allen mentions a slightly earlier reference, but
doesn't quote it. Maybe this is the quote in Bosworth & Toller:
"Carles wæn ne gæþ næfre adune under ðyssere eorþan swa swa oðre
tunglan doþ." (Carl's Wain never goes down under this earth as other
constellations do.)

http://beowulf.engl.uky.edu/cgi-bin/Bosworth-Toller/ebind2html3.cgi/bosworth?seq=161

And the constellations is mentioned much earlier still as 'wænes
þisla' "the poles of the wain" (Metres of Boethius), and elsewhere,
also just as 'þisl'.

Allen: "Grimm cites Herwagen, probably the Horwagen of Bayer and the
Hurwagen of Caesius." Grimm also has a Swiss version Herra waga (The
Lord's Wain?) Or could Her- be a warlike connection to those names
for Óðinn beginning Her-?

Other historical variants: 5 Charlmons wayn, carle wensterre,
carwaynesterre, Charelwayn, Charlewayn, 6 Charle wane, 6-7 Charles
wayne or waine, 7 Charles or Carol's wain(e, Charlemagne or Charles
his wane, wain(e, Charle-waine, Charlmaigne Wain, 7- Charles's Wain.

'charl' is a normal variant of 'churl' form Old English 'ceorl'. For
other examples of this sound change, compare 'dwarf' and the obsolete
'dwerrow' from OE 'dweorg' / 'dweorh', and the doublet 'person' and
'parson'. But 'carl' is borrowed from the Scandinavian form, or in
this case if the OED is right from Frankish, perhaps through Latin
Carolus. The forms in the different Germanic languages go back to two
parallel versions of this word: karl- (ON karl, Fries. tzerl, OHG
charlo) and kerl- (OE ceorl, Du. kerel, MnGerman kerl). *If* the OED
is mistaken though, then this late OE form 'Carles wæn' may well be
due to Old Norse influence (cf. Campbell: Old English Grammar, section
144 for the limits of "retraction" of /ea/ to /a/ in Northumbrian; if
I've understood this right, the form 'carl' would be exceptional as a
native OE development, even supposing Germanic *karlaz had survived
there beside *kerlaz).

LN