Mage is widely considered to be the "king class" of Classic. Being at least mid-tier at every aspect of the game. In PvP, their damage is top-tier, their crowd control is unmatched, and their survivability is decent (particularly if you're Ice). All in all, mages are in a pretty good spot. The only outlier was that going full Fire was not really viable in PvP compared to the alternatives, so that's where most of our changes went.
Fire in Classic was relegated to being an "Elementalist" hybrid spec, going half Fire and half Ice. Combustion was too unreliable to really take over the utility of Ice Block. So we needed to add a capstone talent that could compete. In the end, we decided Dragon's Breath (a cone-based disorient from later expansions) was enough utility and protection to justify the tradeoff without sacrificing their identity as a glass cannon. In addition, we added Blazing Speed and Fiery Payback deep in the tree to allow slightly more protection and more flagrunning versatility in Warsong.
Arcane was always a kind of very powerful one-note spec in Classic. Its gimmicky and cheap and simple and we love it. You trade all the utility in Ice for the most powerful kill confirm in the game on a 3 minute cooldown. Still, in the context of Battlegrounds, it probably underperformed relative to the sheer control of Ice. So we added Arcane Implosion, an ability that makes you automatically go invisible for 3 seconds once your Mana Shield breaks (on a one minute cooldown). This provides a little bit of safety to an otherwise extremely squishy archetype. Overall, Arcane is more or less the same. It has its niche and we didn't change much.
Ice is completely unchanged being the meta spec.