I remember first time I played this game and I hated it since I could not skip cut scenes. I played it some years later and I found out I was actually able to do it. So the question is: Is there any way to skip cut scenes in GOG version? Or is it just random - sometimes you can sometimes not, depending on whatever it depends on?

Why would you want to do that in this game?

Yes, sometimes you can and sometimes you can't. The intro dialogue can't be skipped, while other conversations can be skipped by clicking the left mouse button. Other sequences, like for example death scenes can't be skipped.
However, generally there is a skip function, it just doesn't always work.