Steve suggests it's not Ares because you're literally given a bunch of characters who fall within a spectrum of good. You have Patrick (Ares) who wants to have peace, German Generals who want Peace, evil General and Poison who want death, people who have had their own people taken over by another group of people, an actor who wants to entertain, etc. It's hard to believe that everything is black and white, and the movie wants you to pick up on this and it's absolutely vital that you do.
Her understanding the war wasn't caused by Ares is 100% vital to you enjoying the core of the movie. Ares only whispered, he never engaged in waging wars because you are to accept that humanity is capable of being cruel without Ares. Which is what Diana accepts at the end because not everything is black and white.
The German soliders don't stop because Ares influence was gone -- there's nothing to suggest his existence actually influences people because he literally tells you he was whispering. Everything else is a "story" handed down. The Germans celebrating was because they're glad to be alive. At the end of the day they're still human with families, friends, just because they were on the "evil" side doesn't mean they can't be happy.
Christmas Truce