Would it be possible to change the amulet for this set, as it feels damned near useless unless you’re a mage (& then, a mage that uses Cold Snap).
Currently the fire ring is good for melee (flat melee damage, chance to ignite & increased fire dot), the lightning ring is ok for spells (flat spell damage, increased shock effect & chance to shock on spell hit), so how about the amulet is changed to benefit “throwing” builds? You could give it flat throwing cold damage, increased chance to chill on throwing hits & increased chill effectiveness. That would make it thematically similar to the other two set items (where you have 1 item benefiting each way the player can damage mobs themselves).
Alternatively you could make the amulet affect all types of player skills (melee, spell & thrown), giving it flat cold damage (probably 3 separate lines, melee, spell & throwing, that way you can tweak them individually, given Shield Throw has a massive added damage modifier), global chance to chill on hit & chill effectivness.