Frost is the best by far...
Fire is weak because the mobs in cata are not pushovers like they were in Wrath. They do hit fairly hard, and have enough health that you cant just burst them down with scorch fireblast etc, meaning you are going to take damage. The damage of fire is actually pretty awful, especially as crit scales down as you level.
Arcanes ramp up time is too long because you really do need to cast a few ABs for decent dmg.
While it is true that fire and arcane technically do more sustained damage over longer duration fight, it is not exactly relevant to leveling. Frost has extremely high burst damage with shatter, and on extremely short fights (ie, mob to mob) your 'average' dps is actually insanely high. As frost you literally one shot mobs until like lvl 83 in shatters, and the extra defenses that frost give are simply invaluable. While leveling you have a shatter for almost every mob you fight between your pet nova, actual nova, and cone nova.
Protip for frost: If you use pet nova on one mob, use the 2 FoF charges on another, then shatter the other mob that is still in the actual nova
Elite mobs are generally immune to slows / stuns, in which case Frost has a huge advantage over the other two specs with being able to avoid a significant amount of damage through both the additional absorbtion spell, as well as being able to use a pet for a 'tank'. Engaging with a pet, popping images to absorb hits, then invising to drop agro onto your pet while you continue to turret away damage gives quite a bit more 'free' damage on those types of mobs. Not to mention that you have a second iceblock available, and a ridiculously strong second absorb barrier instead of only mana shield like the other two specs.
You also need to take into consideration that you are basically guaranteed to have some type of pvp encounter if your server is PVP based. Frost is certainly the best at managing mulitple enemies, which is most likely going to be the case as you're probably going to get attacked while trying to kill other mobs, and even in a 1 on 1 situation, frost is still arguable the best pvp spec.
I suppose there is something to be said for leveling with the spec that most appeals to you, but you should also consider how much you value convenience and effectiveness while leveling. It really isn't a competition in those two categories, frost is just simply better than fire and arcane...
Consider this for a leveling spec that is finished at 85
http://cata.wowhead.com/talent#oMZcbMoZdfbGsusd0o (pick your talents with this, or something similar as your goal, and then respec as needed once you actually hit 85)