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But maybe Frost is in Nature School?
Baerskin a lvl 1 Armor 2 Armor Frost -2
Dragonscale Hauberk, Wind Wyvern Hide, Storm Drake Hide,...
What you think about Frost...
I first want to note chitin armor is nature while acid spells are water, so we already have an exception.
If we examine ice themes in common fantasy worlds, then in D&D ice is themed toward water while in Exalted cold is themed toward air (and somewhat toward dark with the abyssal exalted).
The Water school already include two of the most useful attack types - hydro and acid. Both surging wave and acid ball are really common spells that most competitive books include a copy of (even when not trained in water). Nonetheless, I somehow remember someone from arcane wonders saying somewhere that frost is supposed to be a water spell (a long ago, I think in one episode of mage wars Mondays). It was a long time ago, so maybe I didn't remember it correctly.
The Air school already have lightning and wind. Unlike hydro and acid, most competitive books not trained in air don't take lightning or wind spells. Considering the next arena expansion is supposed to include a mage trained in air (wizard), it makes air a possible candidate. [Unless the barbarian VS sorcerer is before wizard VS forcemaster?]
The dark school is out of question, since now that the necromancer counts as one of the best mages there is no chance that arcane wonder will give such a major boost as in-school attack spells. Not likely.
Nature school actually sound like a fair possibility, since the beastmasters aren't the best mages right now (and the druid have enough good in school attack spells anyway). Might give some interesting possibilities for beastmasters.
I don't think there are currently other schools that could be serious candidates for frost
