Your point about the glue of the recurve bow being weakened by wet weather is interesting. If so, that would have tended to limit Mongol conquests to areas with arid climates and would account in part for the Mongols’ withdrawal from their conquest of Hungary.
The Mongols withdrew from Hungary because the death of Uggedai Qa Quan required a quiriltai to choose his successor. Since many of the princes of the blood were on csmpaign in the west, they returned wioth their personal troops. So Batu Quan pulled back to Russia, after laying waste to Hungary.
That process took something like three years or more, with Uggedai’s widow, Toregene ruling as regent. Her efforts to see her son Guyuk succeed were successful, but they resulted in the first cracks in the house of Temujin, since Uggedai had wanted his grandson Siremun to succeed him, and Batu Quan, who held the largest ulus in the Empire not only failed to attend and give his oath, but had fought with Guyuk in the West. His antipathy, coupled with the ambitions of the sons of Tolui, would take the Supreme Quanship from the Uggedids within five years.