Personally, I would only use the Duster Coat while playing as John. It did not seem right to me to see Jack wearing his father's clothes. (Aside from his hat)
But, I do know this, if you complete Remember My Family with Jack wearing the Legend of the West outfit, you feel more like such a badass when Jack walks away and triggers the credits. It is even more pleasing if you do this while it is raining, the darkened and windy atmosphere just gives that last duel with Ross such a kick. (At least for me it did.)
Actually, it was rumored that he got them from a knife fight. That or he could have been attacked by an animal.
Do not quote me on this, I only have heard rumors regarding John's scars.
I saw people talking about it on some forums. Note this was around two or three months after the game was released, so I doubt the forum is still even up let alone active. It was rumored that he got on of the slashes from a knife and the other two from something else. (Possibly a bear as you said) This was because of how the scars appeared on his face.
The slash across the bridge of his nose could have been caused by an animal as it looks more of a rough slash. The same goes for the scar in the middle of his cheek.
The scar going from the middle of the same cheek to the end of his jaw appeared more of a straight and clean slash, like from a knife.
Here is a picture to give a better view of his scars. reddead.wikia.com/wiki/John_Ma…
I personally thought him getting scars like that from a knife fight seemed far-fetched myself. When I first saw them I thought he got them from an encounter with a cougar.
I have come to see John's scars as one of those "unexplainable details". Meaning, you do not know how he got them, when he got them, or why he got them, he just has them.