I’m referring white animal fur-looking thing with black spots, worn as a sort of shawl.
First of all, what animal is that even? Like a spotted snow leopard or something?
Was that garment common among Men of Importance in his day? I’ve seen various saints, potentates, regents, and other Great Men depicted wearing it in various iconography.
ETA: Would the real King George III have worn something like that?
Ermine was a traditional high-status fur; Philippa of Lancaster (sister of Henry V) is documented as having been married in a white tunic with a silken cloak bordered with ermine back in 1406, while the present queen’s coronation robes in 1953 included a crimson velvet mantle edged with ermine. Yes, the real George III would have worn ermine fur, as would other prominent Great Men. (The black spots are the tails of individual animals.)
Ermine capes have a strong enough traditional link to royalty that they’ve named a “trope” on TVTropes, the “Ermine Cape Effect” (that being the idea that kings and queens just sit around all day wearing their crowns and ermine capes, even when they’re just eating breakfast).
I don’t suppose that the Hamilton costume designer was going for strict historical accuracy. But the precise answer to the OP is that it is probably supposed to be George III’s Parliament Robe. That was worn by him during the opening stages of the coronation ceremony (but not for the actual crowning) and later whenever he addressed Parliament. It still exists.
It is not to be confused with the similar Imperial Robe, which he only wore during the final stages of the coronation ceremony (but, again, not for the actual crowning). That was purple rather than crimson. This is what he wears in the Allan Ramsay state portrait.
Incidentally, the Hamilton crown is certainly wrong. That is clearly based on the St Edward’s Crown, but George III never used that, instead only ever wearing an altered version of his great-grandfather’s state crown.
British peers also have robes with ‘ermine’, as do some Oxbridge academic gowns. But this is now usually only imitation, being either miniver or artificial. It has been indicated that the Queen will in future only use artificial fur on new outfits, but this does not affect her Parliament Robes as, being 94, she’s given up wearing bulky ceremonial robes.
It was quite usual for state portraits of European royalty to show them in ermine, to impress their power upon the viewer. Even the Dutch bring out a ceremonial ermine-trimmed robe for the formal inauguration of a monarch - most recently in 2013.
This may come as a shock in this day and age, but picture your Senators, then look at this picture of our equivalents, the Peers of the Realm who sit in the House of Lords (The UK’s upper house in Parliament).
The amount of rows of spots announces the rank of the wearer - Duke getting the most spots.
They only get to wear the ermine at coronations, so I doubt many sitting lords have got to wear theirs (yet).
Although none of the other European monarchs now wear fur-lined robes, most of them do still include them in some versions of their coats of arms - e.g. Belgium, Leichtenstein, Luxembourg, Monaco, Norway and Sweden. As do some Continental noble families. In this respect, Britain is actually one of the odd exceptions.
Not least because the bulk of the hereditary peers were removed from the House of Lords a good few years ago (and of course we don’t know what, if any, differences there might be in the next coronation ceremonials - though one suspects not many, given the people lilkely to have a hand in planning it).
Unless they were being cheap, in which case it would be trimmed white rabbit with dyed spots. Or patches of black fur sewn in. I’ve done this with white and black fake fur for stage costumes - I cut diamonds out of the white fur, and sewed diamonds of black fur in…
So they have these ermine robes hanging in the back of the closet for decades? Wow. And I assume before the next coronation, there’s going to be a brisk business in dry cleaning, repairs and tailoring of new ceremonial wear.
They might even have to get the ermine mallet out so they can patch some bits that the moths have got at. See, its not all beer and skittles being a peer.
That’s why I’ve always insisted on only the finest of long-tailed weasel coats. You wouldn’t catch me dead wearing short-tailed weasel. It’s the patriotic choice for the well-heeled swells of North America .