I just started a new character who has just been to High Hrothgar for the first time but have not yet retrieved the Horn of Jurgen Windcaller. So I am not that far into the Main Quest yet.

My question: is there an ideal time to start the Civil War quests within the overall context of doing the Main Quest?

Do MQ first and then do CW?
Interspread MQ with CW and work on both at the same time?
Does it matter?

Thanks for any clarity/insight.

Doesn't really matter, though there is a notorius bug (not sure if it's been fixed) where a peace council between the two sides is called, but fails because the game doesn't read it properly. Optimally, you'd want to do the Civil War before the peace council missions (You'll get a good indication when it's coming up, FYI.)

If I have completed the Civil War quests before the peace council is called, then what is the point of the peace council since the war is effectively over and Ulfric/Tullius is dead?