I do not think they can go forward because the future has not happened yet. the future can change.
They can go forward too. When Harry asks Hermione why they cannot be seen while back in time, she explains that "Some wizards have even killed their past and future selves by accident." (Rowling, Prizoner of Azkaban). Therefore it is implied Time-Turners can go into the future as well as the past.
I don't think it is implied that they can go to the future as well because that simply means that when they go back in time the past self kills the future self instead of the future self killing the past self.
Most probably, a time-turner allows a wizard to travel forward in time, only as far as the present moment. So for instance, a wizard may travel back in time five months, meddle about with whatever they meant to meddle about with, and (assuming they didn't disrupt the time stream by killing their mother, or some such paradox) travel forward again o the present moment. You can't, however, take possession of a time-turner and go forward in time to events that haven't happened yet.