[color=darkblue]“Over the hill is a forest,” is a variation of, [color=darkblue]“There is a forest over the hill.” It means that a forest (one that we haven’t talked about yet) exists over the hill. Your sentence, “The forest is over the hill,” has a different meaning, because the article the indicates that we have already talked about the forest before.
The structure of the sentence in question results from two processes called fronting and inversion. The real underlying structure of the sentence is “A forest is over the hill,” although we probably wouldn’t ever say it that way.
The processes form this sentence in much the same way a question is formed. First we move the phrase “over the hill” to the front, because we want to emphasize it, and then this requires that the helping verb or the verb be move up in front of the subject.
This inversion happens a lot when we put a negative word in front of the sentence, such as: [color=darkblue]“Never did we go in there.” “In no way are you obligated to do this.”