From what I've read European wars didn't feature much large scale battles of the type done of plains in central asia. Siege warfare, skirmishes, harassment etc dominated.
Anyway the mongols used huge number of horses which would need a lot of grass. It is my understanding that that was simply not available to them in most of Europe.
"It is my understanding that that was simply not available to them in most of Europe."
I hate to break it to you, but Europe has a lot more grass than Afganistan or Middle East. Of all problems, the supply of grass was the least of them.
The main "problem" that kept them out of Europe was that they as people started to change. They stopped being the frugal people living savagely in tents all around steppe. Little by little they become city dwellers and started to embrace luxury and other "decadent" stuff continuously supplied through tributes, enjoying their life rather looking for new conquests. That's how I come to look at it anyway (the Golden Horde).
Anyway the mongols used huge number of horses which would need a lot of grass. It is my understanding that that was simply not available to them in most of Europe.