I think the opposite is true, actually. The original Terminator has a closed-loop storyline (in the original cut of the film you actually see that the factory where the Terminator was destroyed is Cyberdyne Systems):

Time is a closed loop, our fate is sealed, the war against the machines is inevitable.

In Terminator 2, there is no fate but what we make for ourselves. Instead of becoming a war leader, John Connor becomes the true saviour of humanity (huh, "JC," funny that) by preventing the war from happening in the first place. At the end of the film, the war is emphatically not going to happen (again, confirmed in a deleted scene):

August 29th, 1997 comes and goes without incident.

But because Arnie needs to spark some interest in his gubernatorial bid, and because studio suits want more Terminator films, they demand a sequel. But the war was prevented! What to do? In Terminator 3 they conjure up a new future war that doesn't start on August 29, 1997 (because that date has been and gone) but that looks functionally identical to the war from the first two films. And then they utterly betray the intent of James Cameron's hopeful ending to T2, by having Arnie say:

"You only postponed it. Judgment Day is inevitable."

So, to recap: James Cameron initially showed us a fatalistic, doomed view of humanity. Then he flips that on its head and gives us a hopeful ending to the series. And then, because fucking studio suits want a franchise they can milk to death, that hopeful ending is undermined by an even more fatalistic line of dialogue that basically says we might as well give up. Because if Judgment Day is inevitable, why bother fighting at all?