I am a ice wizard, and though my second is death, I know that fire would work great as my second. They are very good together. One of the reasons would be that they would cover up each others weaknesses. If I am battling an ice person, I don't like that they always resist my attacks, sometimes by alot. If I had fire as my second, however, then I would not only be able to hit them without any resisting, but I would also get a boost. The only problem is when the ice or fire person puts an ice or fire shield on. That would be a big problem. It also means that you will get shields for both of your schools. I do not have a death shield, but I do have a fire shield, and fire students get ice shields. That way when you're battling someone that resists your attacks you will not only be able to get a boost out of them but you can shield against them too. And another way that they cover up each others weaknesses is that though ice spells are weak, we have tower shield and that is very helpful for shielding. Though I don't know much about fire, I think that they don't have many ways that they can shield. Therefore, ice provides shielding and fire gives power. Did that answer your question?
One thing I have noticed is how monsters of the opposing element as yours, will try to put up shields. These are usually the single element shields that will block 80% of the incoming damage respective to that element.
One thing you can do, use wand attacks or your lowest level spells to remove the shield, and hit with everything you got as soon as you have recharged any lost mana.
I have recently gotten a bit more "smart" about combat, so shields now are more important to me than power ups. (Especially to those that like to PvP).
There is a vendor in the Mini-Game area in the Commons, for those that do not know, that sells -80% elemental shields for every element (except balance) for 1 training point each. Also, each school teaches a shield combo (2 shields of 2 different elements at -70%) for 3 training points each. By the time one reaches Mooshu, and completes the final training point quest, one will have enough points to get a shield of each element, and ontop of that the "Weakness" card from Balance, and the Ice shield from the Ice school. (I am currently 90% sure you can get the Ice shield from the Ice school.)
I look forward to the new PvP system, and having trained with every shield, I can see my line-up chart and configure my deck with shields against the elements my opponents will use.