Yeah, mages are known to live for long in Arena once the other team has offensive dispels. :b
Without the current CCs / snares we have, we'd get annihilated even faster in Arena. I do agree that it can be over the top with Iceblock on Cold snap, but if CoC/Frostnova shared the same DR there would be nothing stopping melee from tearing us apart in < 5 seconds.
Try duelling a mage and tell him not to use CoC and Deep freeze.