Curious. If you finish this quest will the war to side with one side, capture holds/forts still be possible, after you defeat Alduin and such? In other words, join the Stormcloaks/Imperials and kill either Ulfric/Tullius?

Yes, it is possible to continue the Civil War after Season Unending. I have used Season Unending to make the Civil War Questline significantly longer by giving up Territory held by My characters Faction during Negotiations.

EDIT If You want to, play through with an Imperial and Stormcloak character at different points during the Civil War. The different reactions from Ulfric, Tulius, Galmar, and Rikke are fun.