I've heard several theorists propose that the mongols would face severe difficulties if they had invaded Western Europe at their height because their bows wouldn't survive the European temperament, the glue would become undone, and the wood would rot. How true is this?
Every historian/internet backseat general/what have you who says this, has clearly not been to East/SE Asia in the Summer. The humidity, heat (both of which are terrible for fish/hide glues) and monsoons make for a much harsher climate than anything in W Europe.
Yet the Mongols had no significant issues with their bows when invading Korea, China (esp south), Japan and Vietnam. Part of this was that the Mongols preferred to campaign in Winter, and also because these bows don't fall apart as easily as some people would like to believe.
Koreans and Chinese used composite recurves very similar to the Mongol bow. Also composite crossbows were common in Europe. The crossbowmen in French employ during the Hundred Years War were all armed with composite crossbows.