Possible causes and fixes, from the UESP wiki, Season Unending article:
When organizing the peace council, the dialogue option "I have a message from the Greybeards" may be missing from Ulfric and/or Tullius. This was done intentionally by the developers to prevent various quest conflicts, and generally means that you need to progress further in the Civil War. Some specific circumstances where it happens are:
If you have not yet joined either the Imperial Legion or the Stormcloaks, and you have not talked to Ulfric and/or Tullius since Helgen, you will be forced to first talk to them about Helgen, at which point they will suggest that you join their side of the conflict. To proceed, simply finish and exit the first dialogue, then start a new discussion, at which point the option will appear.
If you joined the Stormcloaks, you cannot continue with Season Unending until The Jagged Crown is complete. This is necessary to prevent the possibility of changing allegiance from Stormcloaks to Imperials after completing Season Unending. If this is the case, complete The Jagged Crown.
During Message to Whiterun (Imperial or Stormcloaks) and Battle for Whiterun (Imperial or Stormcloaks), progress in Season Unending is intentionally disabled because a truce is impossible while Whiterun is actively under attack. If this is the case, complete the Battle for Whiterun before trying to proceed with Season Unending.
It's possible to skip this quest altogether if you've already completed The Battle for Windhelm/Solitude.
Regarding the Stormcloak Civil War quest not proceeding (from UESP wiki, 'The Jagged Crown' article):
If you have both "The Jagged Crown (Stormcloaks)" and "Season
Unending" active at the same time, you cannot advance through Season
Unending with the crown in your inventory.
If playing on the PC, install the Unofficial Skyrim Patch, which will help avoid/fix bugs related to the Season Unending quest, the Civil War quests (including 'The Jagged Crown'), and other related quests.