Adding volumetric fog to an environment will make the distance which
player can see shorter (the fog is blocking your sight).
So I wonder if this mean adding volumetric fog to an environment will have a lower performance cost than not adding it (because fewer objects can be seen so the engine do not need to render those objects blocked by the fog).
Adding volumetric fog will not lower performance cost but actually cost more. Here is a good read from the docs that goes over volumetric fog and its performance costs. But like almost everything else in the engine, you should profile and test for yourself because every scenario is different and so will your results.
Thank you so much for your answer!
No problem, you are welcome!
Thanks