I never believed it to be a provable clothes sharing event, but I was proven wrong with this project. The charcoal hoodie has become Supernatural legend. It has spawned practically a whole genre of fanfic in and of itself, and at the very least has made the idea that Dean wears Sam's hoodies when he's sick widely accepted fanon.
As for the hoodie itself: it's charcoal black and cozier than Sam's regular hoodies. Since Dean is actually wearing it in it's first appearance, there's still room to debate on ownership - but I think, logically, it must be Sam's, since Sam is the one who wears the hoodies in the family.
The Charcoal Hoodie appears first in Faith (1x12). Dean wears it home from the hospital, and keeps it on for the trip to Nebraska and his healing. As soon as he is feeling better, he takes the hoodie off.
In Nightshifter (2x12), Sam wears a charcoal hoodie after he and Dean return to the motel room to review the tapes that Sam confiscated from Ronald. It is the only scene Sam wears it for.
FATE: Perhaps it was lost somewhere in their travels or perhaps it still lies somewhere in the bottom of a duffle bag waiting for the day Dean needs it again.