They encounter a gate and manage to get it open, but during one take, Winslet's gigantic old-timey coat got caught on the gate and she was dragged beneath the water. She managed to wriggle out of the coat, but not before she reached the point where she felt like her lungs were going to burst.
Cameron downplayed the incident as an actress being dramatic, pointing out that Winslet got right back to work and commenting, "We simply let Kate think she was nearly drowning." You know, for dramatic purposes. But Winslet said that she didn't want to look like a wimp, and that the shoot was so excruciating that on some days she'd wake up thinking "Please, God, let me die."
Winslet also had a fun time filming underwater scenes, as she was weighed down 12 feet below the surface of a water tank and given an air supply, but sometimes ended up sucking in water instead. And because she was wearing a dress instead of a wetsuit, she came down with pneumonia. By that point, it's possible that she was actually praying for Cameron's death, but that would be rude to admit in an interview.