Copperhead snakes typically swim at the surface of the water and copperhead snakes swim in both brackish and fresh water and normally hunt around the edges of water, under rocks and logs.
Copperheads swim and do things similar to regular water snakes.
I have however seen a Copperhead snake swim under the water about 10 years ago when I was out fishing in a pond.
It scared the heck out of me then I'm terrified of snakes and have been since I was a little kid.