|Photo: Copyright William Quatman.|
The water is quite static it seems to me. Cougars (pumas) live in a wide range of habitats including seasonally flooded savannas. In Florida the puma is found in cypress swamps and well as other habitats (see range).
In the central-western parts of Brazil's Pantanal pumas usually use the drier habitats rather then the wetter habitats used by the jaguar.
Pumas are terrestrial but can swim and climb trees when needed. See Puma Cat for lots more and Mountain Lion Description.
Associated: Cats that like water.