I'll agree to that as well
But the term 'cold war' specifically precludes conflicts. It is and ideological war between two powers that doesn't typically end up in open warfare. Check it out online through any major dictionary and I believe that's what it'll say. I agree with what you state, it is just that I think you may be confused with the ramifications of the term. Granted, there were conflicts that accompanied the cold war, but by definition that was not a direct part of the cold war.