Pretty much the title, I've been playing a lot of Witcher 3 and as I'm riding through cities with cobblestone roads I'm wondering if back in the day the horse riders had to get off their steeds everytime nature called, or if they just left it there (would it be considered rude?).
While I can't provide an answer for etiquette with dung, I can talk a bit about how late-medieval London kept it's streets reasonably clean of it.
From the 13th century London's civic government had devised a plan for cleaning it's streets. As the City was split up unto 24 'wards', dung removal was delegated in the same way. The cleaning operations in each ward were led by a 'beadle', an elected individual who was responsible for the overall condition of the ward. He was equipped with a cart for cleaning, and by 1357 he was accompanied by 'rakers', who collected the dung and dumped it outside the City (or in the neighbouring ward if they were feeling lazy!). London's government paid for 12 carts and 24 horses to clear the street rubbish across the 24 wards.
In 1385 the City's government appointed a 'serjeant of the channel' whose general brief was to ensure that the beadles were doing their dung-clearing job effectively. As well as this, fines were introduced for dumping piles of rubbish in the streets, so it could be suggested that a horseman was expected to clear up after his horse.
London was an affluent and well-organised city in the Later Middle Ages, and as such, could afford to take these sorts of steps to create a healthy and pleasant civic environment for its inhabitants.