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?
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.