https://www.nps.gov/shen/planyourvisit/basicinfo.htm
It's an on your honor system during the off season and prices are posted. There is a locked drop box to put your money into. No it's not free, they have to pay personnel to clear the paths and take care of the park in general, porta potties etc. We get a season pass which is a very reasonable way to go and if you like to hike often, I would highly recommend.
Come in early enough and it's free!
I don't know when the park opens for the season but I'm guessing you could check their website.
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