Earlier quoted context omitted.
I read a long discussion about this on Quora. What I could gather from that was there were far more castles in Europe than China. Also Europe has too little plains to be able to support a mongol army very long. They each had something like 5 horses. There isn't enough grass for a large mongol army like that. One the debaters claimed e.g. that European castles were very well supplied for long sieges and would run out…
5 horses is quite a bit of food to feed the army... the more the army eats the more grass you have left for the horses... so when the castle is running out of food you have 1 good well fed horse and 1 good well fed soldier who has to win or he doesnt have enough horses to go home i think that wins
Plus you lose whatever advantage the extra horses gave you until you get more—I mean, I'm sure they didn't keep them around just for fun. Greater travel speed by resting them off, extra cargo/loot capacity, whatever their reasons were.