I'm trying to build an ice based Eidolon for my summoner. The concept I'm working on is sort of a magical frozen knight. However, while there are two acid spells and three fire spells, there's only one ice spell, one force spell, and one electricity spell in the entire list. Even worse, the ice spell, Ray of Frost, doesn't scale to level at all leaving my Eidolon doing a dinky 1d3 damage.
My GM doesn't want to use third party material so I'm wondering if anyone has any advice? I really like this concept and I've already built my character but I don't want to be useless.