Origin of "toffee-nosed"

According to the Oxford English Dictionary, the term toffee-nosed is slang that originated in the early 1920s:

1925 E. Fraser & J. Gibbons Soldier & Sailor Words 287 Toffee-nosed, stuck up.

The source of this quote suggests that it was a term used by soldiers and/or sailors. The Sydney Morning Herald reported:

There are theories that "toffee-nosed" (or "toff", and meaning snobbish; pretentiously superior) comes from "tuft" - a gold tassel on a cap worn by titled student at Oxford University. But more credibly - if less tastefully - the origin appears to derive from the unsightly brown droplets that dripped from a gentleman's nose after taking snuff - which of course was only taken by the "upper class". (Ref: Sue Arnold's book Beau Brummell: The Ultimate Dandy [2006])

The Phrase Finder adds that this is a very British phrase, and that it definitely derives from toff or tuft:

The origin of 'toffee-nosed' has nothing to do with the sugary, brown sweet, but derives from 'toff', which was the slang term given by the lower-classes in Victorian England to stylishly-dressed upper-class gentlemen. It was recorded by Henry Mayhew in London Labour and the London Poor, 1851:

If it's a lady and gentleman, then we cries, 'A toff and a doll!'

It is widely agreed amongst etymologists that 'toff' was a corruption of 'tuft', which has a clear aristocratic pedigree, being the ornamental tassel on an academic cap. Specifically, a tuft was the gold tassel originally worn on academic caps at Oxford University by the sons of those peers who had a vote in the House of Lords. They were worn on the celebratory 'Gaudy Days', i.e. the university's twice-yearly feast days (which sound a good deal more fun than 'Dress-down Fridays'). The wearers of the prestigious tufts became known as tufts themselves, even having their own sycophantic crowd of wannabees, known as the 'tufthunters'.

Tufts were variously called tofts, tuffs and, by 1851 at least, toffs. They were already a well-established breed before 'toffee-nosed' began to be used. That didn't emerge until the early 20th century, as in this definition from Fraser and Gibbons' Soldier and Sailor Words, 1925:

Toffee-nosed, stuck up.

The 'nosed' part of 'toffee-nosed' appears to derive from the allusion to the haughty toffs, who stuck their noses in the air when faced with the hoi polloi.

So someone who is toffee-nosed is a toff, or one who sticks their nose haughtily in the air.

I think the derivation is the other way around, since I find some data of "toff" but not on toffee nose. Etymology online says:

lower-class British slang for "stylish dresser, member of the smart set," 1851, probably an alteration of tuft, formerly an Oxford Univ. term for a nobleman or gentleman-commoner (1755), in ref. to the gold ornamental tassel worn on the caps of undergraduates at Oxford and Cambridge whose fathers were peers with votes in the House of Lords.

Another source suggests the rather unpleasant explanation that it derives from the brown drops that dripped from the nose of a snuff taker. I'd go with the former, but mention the latter to gross you out on this lovely Saturday.