The strongest and most reasonable counterclaim to the claim that "The Summer Olympics are more important for athletes than the Winter Olympics are" is: "For many winter sports, the Olympics serve as a world championship competition; most summer sports have separate championships."
This sentence presents a clear point that highlights the significance of the Winter Olympics for athletes in many winter sports, framing them as crucial competitions akin to world championships, which counters the idea that the Summer Olympics are inherently more important.