Ah, fine finger motion is SO much fun! And look at the show Mama gives her when she uses her fingers on Mama!
You're right, she's not deliberately trying to give you pain. She's just doing the best she can (she thinks!) with what she has.
So say, "No, we don't pinch hair; here's something you CAN pinch," and give her what's handy and safe: a teddy bear, a towel, a... (you fill in the blank). "No, we don't pinch people; here's something you CAN pinch." Let her do her practicing, but on something that won't cry or say, "Ouch."
Does she like you to hold her? Maybe if you set her down when she pinched, she'd decide this game isn't such a great one.
And maybe you want to, um, get your hair cut? No, forget that - you'd have to get it all shaved off to keep those little fingers from being tempted!