Both Arcane and Frost have their do's and don'ts. That's just a fact. Arcane has huge damage output due to consistent mobility and some nice blanket CS. Both important in some settings. Cotus +1.
However, Frost's role is different, as Rifvader stated. Support, in a manner of peels, slows, chills, roots,... If played well, you can hold a whole team off your FC and get him time to get away. Sure, in AB, which you usually play, Frost has a less significant role, but it still has proven me his worth. The CoC root can't indeed be used to get a Shatter, but rooting a Warrior, Ret Pala and some Rogues, hitting on your FC, with one single ability, isn't too bad.
I've played both specs, during a long period of time, and its clear they are both viable. As everyone knows, Arcane is more offensive, Frost is more supportive. Always have been like this, and it still remains the same.