Even though Cara Greenberg has said that "design never fails to capture the spirit of an age", I have never personally encountered any recognizable design from that period that actually relates to the issues you mentioned but you will probably find more examples of artists work from that era that dealt directly with those issues.
The closest designed items that I could recall that was influenced by the Vietnam war were those portable radios and tv made by Sony and other Japanese manufacturers in the mid 1970s...I just don't know much about if the manufacturers or the consumers who bought those were taking a political stand or something.
It is not going to answer your post but if you are interested you may want to look into this book called 'Op to Pop, Furniture of the 1960s' by Cara Greenberg published in 1999.
You should also look into Roy Lichtenstein's 'Whaam' from the early 1960s acquired by Tate Modern in London and see if there is something in that work that relates to the issues of the Cold War era.
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