How crucial was the role played by heavy cavalry in medieval European militaries ? Were there any battles that were won primarily by heavy horse action?

Uh, well, for most of the Medieval period, kind of all of them…up until Crecy, Poitiers, and Agincourt, the knight ruled the battlefield and it took a while for people to adapt. Even then, it took until the early modern military revolution for giant blocks of shot-and-pike and artillery for heavy cavalry to be pushed to a secondary role.