Why was the cold war a war nobody could win?

As you suggested Cold War is not war. It is a misnomer. It is a grand military stand-off; a full dress rehearsal with all weapons ready to go - "across Europe". Such a situation was unlike any other in history. It could have escalated into a full-fledged war. So there is a Win in that. Who wins is who doesn't blink first. The Soviets chose to lose. It is their same attitude that a submarine commander, Vasily Arkhipov displayed in the thick of naval confrontation in Cuban missile crisis. Both super powers displayed utmost restraint in directly cofronting each other. It was reflected well in their European stand-off that was totally error-free, which is a remarkable technological achievement. The world is grateful for them, for that. 
Things were different outside Europe, where wars were fought through their surrogates often in the same (Third World) country, as their blood is far more expendable than the European. These wars were as bitter, messy, furious as any other war plus they are much capital intensive. By now an impression has gained momentum over half a century that America always is spoiling for a fight & reasons (excuses) are secondary. Because of this proclivity of theirs they developed a coterie of friends who look up to them to solve their (domestic) problems. 
SDI (Strategic Defense Initiative) launched by Reagan, but turned down funding by the Congress could have been the biggest engineering project. If we look at it against the steadily escalating costs in dollar terms (inflation correction is really no help), putting a Man on Moon that includes the development of Saturn V rocket was the biggest engineering project in American history. Earlier Manhattan project if strategic savings in War cost was considered too, could have been that. So far as its technological reach, Historical impact & etc go, nothing beats project Manhattan.