Yeah, it really depends on what you plan on doing with your maging career.
Frost- You can snare the hell outta people, you get a leet-sauce elemental, you get ice barrier, ice block, and you survive way longer than any mage should xD.
With all this things as a plus you also have several minus's you will never do as much straight up damage as a fire specced mage, but you will get close if you learn to play it right, and you will also usually need better gear than those fire or arc fire mages out there in order to get get completely lolpwnd by them.
Fire-you kick the **** outta most things that try and come up to you, you get 2 extra dazing attacks with blast wave and dragons breath, you need lotsa crits, and you kill **** FAAAAAST.
Only downside is, if you dont kill em fast, your dead, period.
Arcane-you will almost never, ever, EVER see a mage go full arcane, it really just aint too great, but arcane is an incredible buffing tree, so whether you chose fire or frost your really gonna go a little into arcane (possibly not) but this tree is really only for buffing, and if you do go 50+ into arcane, your gonna be going fire with it. Once you get that far into it your not gonna have too much use with ice.
I hope this helps with your query.