It's not a super big deal, really It really isn't. Legend totally doesn't care at all about it, obviously. (Except he sort of does. He's always worn a hat, before he was a hero, before he picked up the master sword, before he can even remember).
Uncle Aflon just got into the habit of putting a hat on his head when he was a baby, because the village women always said it was important to keep little ones warm and most of the heat escapes via the head. So, since he was tiny, Aflon always helped his nephew get dressed and then popped a hat on his head. And even after Legend was old enough to do it himself, his Uncle still always tucked a hat on him because Aflon sort of just got accustomed to it and Link grew out of everything else already so he's just keeping this one small thing as long as he can.
So legend literally has gone his whole life wearing a hat and suddenly not is...weird. It's not a big deal, but also, he's oddly uncomfortable, and cold, and there's something missing all the time and it bugs a tiny little part of him.
The rest of the heroes' notice something is off. They push. legend of course tells them that it's nothing, he's maybe just slightly sort of out of sorts. Maybe he doesn't even realize that's what's wrong.
But then, maybe as a joke? Maybe just because, maybe because Legend's being extra grouchy and they just were trying to get him to shut up, someone tosses a spare shirt or a scarf/pelt/cape at his head one evening and it just sort of clicks. Legend's mid-way through saying something and then he gets hit literally and mentally with the realization of what's wrong and just goes oddly quiet.
He doesn't yank the offending article off and throw it back like normal either.
Wind's the one who asks if he's missing having a hat, sort of as a joke. But when Legend just nods, looking totally and completely confused...well
Well! The rest of the chain all have various hats they never cared for, or don't use, and if Legend would like a new one then he has his pick! (Technically, Legend's got plenty of hats from Hytopia, but he doesn't tend to carry them around and besides, he wasn't thinking about it because they're not The Hat).
All this as an excuse for Legend to just...get to wear some different hats. Maybe he does pull out some of his own (The Kolkiri hat is a favorite of mine, he'd be so Snufkin), but there's also a couple others I think would be fun. Twi's silly gilded hat thing from his fancy rupee draining set looks like sort of a crown with a hat attached, and if you go for the Twins Theory then it's sort of ironic. Hyrule has his red one that almost exactly matches Legend's jerkin, and he's only too happy to offer Legend something for once when usually it's the vet lending him a tool or new boots or something of that nature.
But the one with the biggest collection? Wild, obviously make this post TotK if you want the most options.
For fluff, maybe Legend realizes that Ravio's hood is actually like....really comfy? Ad smells like him, and thus like home, and thus he's oddly calmer and more sedate with it.
Crack? He unironically loves the CeCe hat, and Wild gets such a kick out of that that he just begs him to keep it. how he keeps the thing balanced in a fight in anyone's guess but he's slaying
Angst? The Royal Guard's Beret is oddly comfortable and Legend actually really likes wearing it, but whenever he catches his own reflection he gets that lovely little reminder that he is, in fact, from a family of knights, a family that's all gone and who's legacy he's failed to take on like he was supposed to or maybe he realizes he looks like one of the knight Uncle used to hang out with, maybe he used to steal their hats after big functions when he was a kid, when the knights would be all dressed up when they visited and the beret was too big on him then but the captain of the guard would fix it for him anyway with this soft little smile, and the memory of that just makes Legend's chest ache (especially if Wild or Wars keeps adjusting the hat for him now when it slips or smth)
Anyways, thanks for coming to me TEDTalk about legend and hats I guess