There's a nuanced point here that looking at GDP % vs inflation adjusted yields different results depending on the range. For example, from 1982-1990, military spending was up, even after adjusting for inflation. It was actually 1990-2000 where military spending actually decreased, both before and after adjusting for inflation.

Compare that to GDP % which would indicate a steady decline in spending. So now we very much do have to examine GDP here in order to look at the argument specifics if we care about 1982-1990. With that said, the cold war ended around 1991, so the military stagnation is more or less in line with the cold war ending. The context missing on the original claim is simply that spending shot right back up once American mucked up and got itself stuck in the middle east, being involved in the deaths of hundreds of thousands of people.

But hey, none of this relates to the original post at all really - that claim was not actually doing any lifting in the original argument other than to serve as a light illustration of how the military spending is never cut in a significant way, and that is generally true save a small exception from 2011-2015. The best that can happen is an effective slow cut through stagnation. And all of THAT is just to say that the government gets pushback when trying to walk back policies.

So did it ever really matter how the cold war affected spending here? What's the point of calling this super nuance out?