We first see this coat in The End (5x04), when Future!Dean is wearing it. Dean himself doesn’t pick it up until later in S5. It may, in fact, belong to Bobby, as Dean finds it in Bobby’s basement after he escapes from the panic room. It’s a green utility coat with a military feel to it. It has two very large breast pockets, and hidden side pockets.
Brand Information: Alpha Industries M-65 (unmodified).
In The End (5x04), Future!Dean wears it for the entire episode.
In Point of No Return (5x18), Dean finds it in Bobby’s basement after he escapes from the panic room. He wears it until Castiel beats him up and brings him back to Bobby’s. Sam (I’m assuming), removes it at some point while transporting the unconscious Dean from Bobby’s bed in the living room to the cot in the panic room, because he wakes up without it on.
FATE: If the coat did belong to Bobby, then it may have burned along with Bobby's house in Hello, Cruel World (7x02).