I ran a Kyurem team with these sets on the Kyurems:
Kyurem-B @Lum Berry (probably change a couple to mental herb)
Trait:Prankster (Snow Warning on the lead though)
Nature Power is to avoid being walled cold by steels (while getting priority and not interfering with Assist), and Dragon Tail to phaze out other troublesome opponents. Sadly (or perhaps fortunately for facing it) there is no reliable way to use the STAB on ice attacks. There's a pretty small list for moves not selected by Assist (and Magic Coat is not on that list), but playing around with Destiny Bond or something might get some results.
Prankster simple beam can neuter Contrary pokemon, but the problem is using it before boosts happen. Tanking the +2 Draco Meteor/Overheat/etc. just to use Simple Beam is risky or downright suicidal. Unaware pokemon survive better, but wouldn't themselves benefit from the Simple stat drops and don't have priority. That would make it viable for something else to switch in though.