From Rebirth of the Night Wiki

In Rebirth of the Night, players can swim by moving in the water, holding the run button will make the player adopt a swimming position that makes them move faster and occupy only 1 block in height. Theres currenty not any penalty for swimming in cold waters. When a player is underwater, a bubble metter will appear in their interface, from which point they have 16 seconds until it depletets and the player starts taking drowning damage.