Two questions:
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What happens to all the hats that get thrown onto the ice?
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Do you come to the game wearing a “disposable” hat, in case you have the opportunity to fling it onto the ice?
In at least several cases I’ve seen, the hats get collected and delivered to a local charity. I’ve also seen minor league games where you are allowed to get your hat back if it’s clearly labeled as yours (no trade ups ;)). More here.
As I have never tossed my hat (or anything else) out onto the ice, I can’t speak to your second question.