Like the Song invasion?
(that said, they crossed mountains and fought in the highlands quite well on most occasions. But sometimes the ratio of forces didn't work well for them)
They did take a very long time to deal with the Song.
But yeah, the Mongols were tough even in the mountains - just that if I had to pick somewhere to play to their weaknesses (within Europe), that would be it.
Europe doesn't have jungles, which would be the best of all possible terrain to play to Mongol weaknesses. Or large scale swamp.
Strategic use of dyke breaking in the Low Countries or the like will seriously interfere with the Mongols, although their speed makes applying that difficult. I don't know if it would be impossible for anyone to counter it, but it would take an army prepared to a level OTL European armies really weren't.
Another reason I think for them not being able to storm Europe's cities efficiently in '42 (as opposed to 36-41) was that besides having very low numbers themselves they ran out of auxiliaries/press-ganged arrow-fodder. As Catilina mentioned, they already devastated Hungary so there weren't sufficient amounts of local infantry that could be thrown at castles the way they were in China, Caucasus and Russia, and they likely ran out of auxiliaries brought from Russia with all the rapid sieges in '41 and didn't have enough forces IN Russia to be able to grab more and bring them to Hungary in one season.
Plus supposedly the Mokshans tried to defect to the Germans so Batu had them all killed, presumably they were to be the aforementioned arrow fodder.
And if Batu never managed to raise a large force from his ulus after this, that suggests part of the answer to the "and what broke down later" - though one wonders about the infantry part of the arrow-fodder department, since they could have just drafted more Russians.
(I think Batu was left with a mere 50,000 after the division of the Empire, of which only one tumen or what remained of it was Mongols, the rest were probably Kypchaks and the like. Which could be an estimate you asked me for in the other thread, if it's one rider per "yurt", roughly multiply by 4 or 5, so something like a quarter million Kypchaks left on the steppes, or slightly more than that?)
Interesting data, thanks.
I wish I knew more about this - there seems to be quite a lot of potential AH material here, if we do away with the Mongols one way or another. But being monolingual in English of all languages is extremely inconvenient when studying Eastern Europe - even if probably written with a bias you couldn't cut with a saber, at least German say would probably cover more than the English speaking world does.