Quite a bit. All of the trails in the nf of nfar are actually old miners roads. I recomend the ones from euchre bar down to stevens trail. When you get to the bottom of the canyon, you can still see hand stacked cobble walls and huge tailing piles left behind by the old timers.
Another word of warning: when you combine high gold prices with an unstable economy, you get homeless camps along almost any gold bearing river. I live in colfax and help out at the mining shop there, so we see and know these guys as they come in to sell their gold. For the most part they are just people down on their luck and trying to survive; they are not bad people. With that being said, gold has a curious effect on people and they can act unpredictably. Watch your ass any time you camp off the beaten path. Be aware.
Kris
P.s. these trails are rugged enough that they dont see a lot of prospecting. I know people who claim to pull half ounce to an ounce a day out from this section of river. I personally have only been down pickering bar trail, and it took 35 minutes to the bottom and a hour and a half back up with no gear. Have fun and be safe.