I see Hermetic society is largely peaceful, too. Wizard War is dangerous and hard to pull off, what with mages being able to fade literally off the face of the earth and living right next door to other magi. I think it is limited largely to ego-fights where both sides actually want to face off. Even a powerful wizard will find it very hard to find a magus that escaped to Arcadia, or to a secret regio only a few know about, has flown off and hidden in a cave in the Carpathian mountains, or took up temporary residence in St. Peter's... And when he does find him, he will find his foe equipped with a home advantage, allies, and an escape plan. Usually even the mighty wizard will have weaknesses in his defenses, and his opponent will set traps based on them. No, I don't think a resourceful opponent that is determined to survive the WW would be outmatched, almost regardless of his opponent. While some violent magi or egomaniacs will pursue them, nearly all conflicts will be taken care of by other means.
In some Tribunals, however, things would still be rather violent. In Normandy I think looting other magi's equipment outside of a covenant is fair-game, and certamens and violent duels of all sorts would, I reckon, be common. In the Rhine the Quaesitors are not respected and so crimes can be committed quite easily, with politics rather than law determining what is allowed. And so on.
I see the Order as largely a loose collection of eclectic traditions, each pursuing its esoteric goals. From Merinitia magi who seek to create great fables to Bonisagus magi who study Magic Theory for its own sake (like a person might enjoy learning history or science), most wizard's goals are somewhat, ehm, detached from practical considerations.
Since most of these mad schemes do not involve other magi, at least directly or by coercion, conflict and therefore violence is rather rare. The most likely source of open violence flaring up is through Houses devoted to fostering violence or conflict, such as Tytalus or Flambeau or in some-stages Tremere. These are calculated acts, if sometimes miscalculated. This also means they are rare.
Also due to the same background, cooperation is common in small groups but rare in the Order as a whole. Criamon magi may cooperate on a plan pursuing the Enigma, but only rarely will this plan have any relevance to the Jerbiton Iconophiles seeking to preserve works of art. Bjornaer magi may cooperate with Durenmar against the faeries of the Black Forest, but will have little in common with these scholarly savants. The order is too fractured and idiosyncratic to form more than temporary, ad-hoc, alliances, and the power of secrets and self-concealing nature of Mysteries means that even these will be tenuous and rare.