Director James Cameron offered DiCaprio a choice: filming in ice-cold water (that’s not an exaggeration, as it implied adding HUGE amounts of ice to it) or using computer-generated images – CGI – for his breath, which was supposed to condense in front of him.
At first, DiCaprio chose to soldier on and film in cold; not only did this produce breath condensation – realism – but also induced actual shivering. Notice I “At first”? That is because, shortly thereafter, the cold reality (pun intended) of filming in such conditions set in – filming under such conditions is extremely difficult, not to mention painful!
DiCaprio decided he could act the part of a man dying from cold while not actually tempting that fate in real life, and accepted CGI breath being added.
So the answer is, “The water was bitterly cold – at first. Then, not so much.”