Sylvanas prompted the idea of war to Saurfang and he rejected her initial arguments. He convinced himself later by remembering Genn's attempt to kill Sylvanas and his attack on the Horde fleet in Stormheim. He often reflects in his internal narration about how happy he is to be going to war.
He is in this regard actually a moderate as no sooner has he announced to the army he's leading that expected to be staying in Silithus that they'll be conquering night elf lands that they start cheering and love it. The average Horde member is pro-war and pro-Sylvanas even as of 8.2. It's in 5.3 8.2.5 that this might change as Varian Jaina mentions waiting for Vol'jin Saurfang's rebellion to take root.