Here in Late Medieval Czechia we had a militant reformation movement called the Hussites. Of course, the rest of Catholic Europe sent in several crusades to crush the heretics, without much success.
One of the many reasons why the crusaders failed were so-called Wagenburgs [0]. Basically, the Hussite army would be underway with very heavy wagons and, if the scouts brought back information about an approaching enemy, would build a provisional fort out of them fairly quickly. Such a fort could not be swept away by a cavalry attack and if the defenders had enough guns (and by that time early firearms were already used in Europe), the knights tightly packed around the wagenburg would present a perfect target.
Plus, there were kids under the wagons with very sharp scythes, hacking at the unprotected horses' legs just in front of them, just as you mention.
[0] https://en.wikipedia.org/wiki/Wagon_fort#Czechs_and_Hussites
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[1] https://ageofempires.fandom.com/wiki/War_Wagon_(Age_of_Empir...
Knights did loose horses though. They all took multiple war horses with them to battle (a "lance" usually consisted of one knight, multiple warhorses and a regular horse for travel/supplies and several servants). When they lost their horse, they fought their way back to their own side and got on the next horse.
Oh interesting, so it was basically expected? Not a force majeure? I always thought losing a horse back then was a really big event for the knight, borderline tragic - a big financial loss, a highly increased likelihood of dying (getting stuck under the horse etc etc)
The most common reason for loosing a warhorse is probably not that it was killed. It was that it was wounded by archers. In that case you can ride back, swap horses and join the cavalry again. And tend to the wounded horse after the battle.
Oh please do tell us more. How and where do you do the re-enactments? I'd love to visit (once the pandemic is over)
So they would be vulnerable, but the horse itself has a vote.