There is a picture on Imgur where someone is saying that Qrow didn't put that cut on Winter but she was battling him when the cut was spotted:
So what? Had it been there or did Qrow cut Winter?
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No, Qrow did not cut Winter, because no one cut Winter to begin with.
Someone needs to get better at Photoshopping, because in this picture from Volume 3, chapter 3 there clearly is no cut on Winter's shoulder.