the idea of cold rinse is that it would help blood circulation in your scalp. And also, the hair becomes less oily if you do the cold water rinse.
It does not really matter whether it is 2 or 3 minutes I guess. I do not really time myself. Before the cold water rinse, you should first rinse your hair with warm water well enough to get rid of shampoo, etc.. then the cold water rinse.. then the vinegar rinse. and conclude with a short cold water rinse again.
the vinegar dissolves any shampoo that may be left in your hair.. It balances the PH of hair. Vinegar works great against the oil buildup on scalp as well..