You do not see Deer swimming often and when you do it is normally pretty shallow and docile water. I found this one near an ocean inlet in 30 feet of water and a swift current! She must have been a strong swimmer with a good bit of luck.
You can't tell by the picture but this current rips and just around the corner it increases speed as it dumps water out miles into the Atlantic ocean.
This deer should take a break after this life threatening feat!
Why do you think it went across that body of water? Food? Get away from Predators?
Hard to know but I think that they are looking for a bit more food. It also could be a seasonal migration of sorts because I see them do this in the Fall coming from the mainland.