The weapon states it buffs +43 spell cold damage but I believe it’s incorrectly coded as regular spell damage not limited to cold.
I’ll demonstrate it with Infernal Shade, a fire spell.
There’s nothing on Frozen Ire that scales with Infernal Shade yet the damage increases fivefold.
Likely the Ice sceptre base does this as well but I don’t have any to test.
Let me know if I’m missing something.