Does exist but seem pretty rare, can be found next to or in water tiles/rivers.
The Swan icon in the game
A swan
Extremely difficult to hunt due to it being in the water. Tracking in the water is like trying to knock out a boulder. You also can't sneak and swans fly away upon detection, making it not worth the effort to hunt these majestic creatures.
Kill a sleeping swan at one step
A swan produces about 17 cuts of meat,swan fat and swan-skin.