Sailcloth Shawl
So I was paroozing the Zelda Informer forums earlier today and found something interesting. This picture, I think, explains a lot.
I think this gives a nice insight into the order of some of the events in the beginning of the game. It also shows that Link's sailcloth is in fact Zelda's shawl. I think this means that Zelda gives it to Link before they go on the bird ride that ends in tornado. I personally think this was a really cool move on Nintendo's part.
On a side not, this also makes me think that maybe those sheets with the crests everyone has on are sailcloths. :O
Credit goes to ZI forum member GestaltReplicant who says that credit goes to a Deviantart user. :S