Harry, Ron, Hermione, and Draco are disciplined by Deputy Headmistress Minerva McGonagall for being out of bed and out and around the castle after curfew. As punishment, the four are sent to track pools of silvery unicorn blood through the Forbidden Forest, looking for dead unicorns. Hagrid is set to supervise the four in the forest while they complete their detention.
In Potterverse, magical creatures are invisible to Muggles.There are a few exceptions. If you count the owls, both Muggles and wizards can see them. In Fantastic Beasts and Where to Find Them, there's quite a few instances of a magical creature being seen by a Muggle.
I can't recall reading anywhere that the Forbidden Forest itself is invisible to either wizards or Muggles. The closest I can come is from Goblet of Fire -- in it, Hermione explains to Ron and Harry about what Hogwarts looks like to Muggles. Hermione explains that Hogwarts looks like a bunch of broken down ruins with a Danger! Go Away! sign in front of it. That would indicate to me that Muggles cannot see the Forbidden Forest.
But that's from the book.
I can't recall an instance in any of the Harry Potter movies where the Forbidden Forest is invisible to either Muggles or wizards. I do not believe it is invisible in the movies. What is inside the forest, however, likely varies -- Muggles probably cannot see the creatures inside; wizards probably can.