It was never flat out said, but Kyle indicated the war was won. Look up the T2 alternate opening that was never filmed and it was clear.
You have to understand a few things and when I say all this it's without T3/TS.
In Terminator (which I thought was the brilliance/uniqueness of it) Time can't be altered. It is an interesting theory as well. If someone actually made a time machine, that means in a linear timeline it always happened that say Dr. Smith made the time machine. So of course he will go back in time, that means that no matter what he always went back in time. Hence time can't be changed. Because technically as some have said, if time travel exists, we would be seeing visitors if that was so. So with Terminator, Skynet sent back the T-800/T-1000 as he was dying quickly to kill John Connor in the past. Then John sends back his protectors. And oddly enough, because of this time travel, fate happens. John never had another father named Joe Schmoe. It was always Kyle Reese from the future. All the dialogue and pictures so on so forth always show that John's father was not from this time. So Skynet really created John in that sense. As well as he created himself always. Because Skynet sending back the T-800 and it getting crushed leads to the technology that builds Skynet in the future by Cyberdyne. So it's cyclical, and it will always happen that way. There is no "alternate time lines" or "delaying" things.
T2's original Future Coda ending which you can find on youtube I'm sure. Showed a happy ending and Sarah talking about the new future. But Cameron cut it realizing it made no sense, and that they could not change the future. Because a future without Skynet means no Time machine, which means no John Connor. If Skynet (dies before 2029) so does John, and vice versa, they rely on each other and the war and the time machine. So in 1997 no matter what Judgment day happens. So if we were to have another T3 being the rise of the machines which I would like to see, it would have to take place in 97.
TS ignores this many times as does T3. But Kyle said in T1 he was born after the war. And in T3 Judgment day is "pushed back" to 2003/2004. So in TS he was 15 years old in 2015 which means he was born before the war. Which is not the case. However most indication is that Reese was born in 2000 or so, but it was "after" 1997 the real date of Judgment Day.
So in T2 with the alternate opening Cameron cut because he realized that it had all been said in words in T1, and so doing this would take away the suspense of not knowing the T-800 was good this time, and it was expensive lol. The original scene showed the T-800 from T1 being sent back (or indication that it had minutes earlier) and that the T-1000 had been sent back as the bust down the door pretty much. So they quickly send back Reese, and then John goes into a giant freezer where there are hundreds of Model 101's, and he goes up and down (I always loved the sound of this scene) to the identical 101's, but it's like he is searching for the right one the one he knows is the one he met as a kid, and he picks one, and then it goes through time and they destroy the place.
There were no multiple TDE's, only one, Skynet used it as a last ditch effort but was shut down quickly after. Maybe later I will try to find the concept art/part of that script. It's online I know.
So the T2 ending is the way it is now because he realized that it really would not end like that.