I'm a mage myself, levelled from 1 to gadgetzen (i think 45ish) at fire, then frost the rest of the way to 80s. Ever since the eternal water glyph came out (
http://www.wowwiki.com/Glyph_of_Eternal_Water), frost is definately the way to go for levelling up, at least until 70's (Arcane is another option here, but dont know about that).
Comparing fire to frost, Fire have a long ass nuke, you gotta sit down to drink every three to four mobs(1 water = 30 seconds = 50% overall mana back), if you two mobs gang up on you, you're not going to take them out. Frost however, has Frost Barrier(
http://www.wowwiki.com/Ice_Barrier), to survive more than two mobs, an extra frost nova if the frost barrier runs out (
http://www.wowwiki.com/Shattered_Barrier), massive slows so the enemy is at 20 - 30% life by the time he actually reaches you (without water elemental).
Arcane is NOT an option until you receive arcane blast at 64, before that you'll have to use Arcane Missile which sucks even worse than fireball.
TL;DR: Fire sucks, go frost like everyone tells you to.