Did either the USSR or USA believe they could "win" a nuclear exchange and if so, why?

Probably only the delusional.

The Short answer is, No,... that's why the policy was called "Mutually Assured Destruction".

That's why they tried so hard to avoid Nuclear War.

I'm familiar with the conceopt of MAD. Surely someone in Soviet High Command thought, " I think we could win this thing".

None of us are qualified remote viewers and even they couldn't answer that question for you.

There's little sense in "winning" if you are dead, or trapped underground in a bunker for the next 100 years or so.

Originally Posted by senojekips

There's little sense in "winning" if you are dead, or trapped underground in a bunker for the nest 100 years or so.

Agreed. Plus, given the number of nuclear weapons both sides had, neither side would be much more than a smoldering radioactive crater if the bombs had dropped.

Wasn't it China who thought they could win any nuclear exchange, because of the numbers game?

In 1982 I heard from a Navy Captain who used to command a submarine that we could win a limited Nuclear war with the Soviet Union. HOWEVER, after sitting in the El Morocco bar in Naples talking with a Soviet sailor I seriously doubt either side would have own. No Mutual destruction, just mutual death.