Thank you. If the idiom is known virtually unchanged across virtually all slavic languages, I would perhaps naively locate it some time before the Hungarians separated the north from the south. So it would be closer to the king Arthur rather than Henry. ;-)I'm inclined to think it's probably "foot", and the same expression exists in Czech, Slovak and Russian (except in Russian it's a "wide" foot). The origin isn't clear. According to this (junior.ru) Russian source, in the Middle Ages King Henry II of England had a growth on his big toe and had to wear shoes with long curled-up front ends, and the nobles then imitated the idea. But we don't have any similar phrase in English except, maybe, "live the high life", which has nothing to do with the length of one's shoes.
That's why I asked about it in the first place: In Polish the word 'noga' ('leg') also exists, and the inflected form 'nozi' is quite consistent with the Polish 'nodze' - and even more so with what I would expect it to sound in Czech or Slovak. In Polish we say about 'high foot', ('stopa', 'na wysokiej stopie'), but such semantic shifts are quite common between the languages, so I was curious it if was a slightly different idiom or a narrowing the meaning of 'noga' to mean only the foot.I've always interpreted noga in živjeti na visokoj nozi as 'leg' rather than as 'foot'. Might be because noga is prototypically 'leg', rather than 'foot'. It was quite a surprise to see 'foot' being used in other languages' equivalents of this idiom!
In the shed of the discussion, the latter considers only Slovenian, as far as I can tell.As for the origin of this idiom, I remember hearing once that it refers to the old practice of nobles wearing high-heeled or platform shoes (cf. the famous image of Louis XIV in the article). But it seems to make more sense in languages where it's a high leg/foot (only Croatian, Macedonian?) than in those where it's a big leg/foot (all others?).