Some additional information has been found surrounding Zombies on Black Ops Cold War. There are very short, yet important images in the trailer that should not be overlooked. These small snippets can provide clues surrounding the storyline.
Zombie mode trailer
Further details were revealed on the battle.net page for Black Ops Cold War. On the bottom of the page, a description of the mode can be found. It will take place during the same time of the campaign and maybe there will be a connection between the campaign and the zombie mode which would explain why we would see a person strongly resembling Grigory Weaver.
For the first screenshot, we can see a character who looks a priori to Grigori Weaver. Nothing has been said yet as to why he's in this trailer.
For the second screenshot, there is a woman with a sort of scarf around her neck, no information has been found about this person and a mystery is hovering over her for the moment.
For the last screenshot, a luminous ball that looks like a sun or a moon can be seen. Two soldiers are watching the glow. There is also a message in writing that makes you think of calligraphy, but not legible enough to make a translation. They look like Russian officers, because their clothes are the same as Soviet uniforms during the Cold War.