balance wand basically help any kind of wizard but as far as a balance wizard you might as well use any wand bc a balance wizard is gonna always use his/her blades if they try to wand an enemy.
The "someone" who told you that an Ice school wand would benefit a Fire school wizard...did you understand what they were talking about?
Fire school gear, in general, may favor doing damage more than resistances, and later on, Critical Block. The purpose of using an opposing school's wand is to benefit from the extra Blades circling your head in a duel, and to remove a Weakness spell and/or remove a Tower Shield w/o consuming your school's Blades/Traps. Another benefit, in the later levels, would be the amount of Critical Block an Ice school would give the wearer.
While it is true that ANY school's wand would allow you to activate your Balance Blades, and an Elemental, or Spirit Blade, consider the other statistics of the wand. Are you in need of a bit more Critical Hit, or Block? Do you find you are needing more Power Pips at the beginning of a duel? Examine not just the school, but the overall benefit to w/e wand you decide to use.
Balance doesn't really benefit from using off school wands because their blades are used anyway. The plus side of this is that you can take full advantage of using more powerful same school wands like Hades and the Hallow's Guitar for critical boost. If you are looking for Block, then there are Ice wands in the card packs that have high block. That is likely what your friend was talking about.
I have 2 accounts and always run 2 wizards at a time. My Balance wizard quests with one of my Storm wizards. Right now I just happen to have a death wand that I particularly like so that's what I'm using.
But typically I would equip the Balance wizard with a Storm wand to burn off any storm shields that opponents might throw on themselves.
Basically a lot of it will depend on who you're questing with, or if you're questing with anybody. If you're just going solo, the school of the spells the wand casts doesn't provide any benefit. In that case just look for the one that provides the benefits (critical block, etc) you most want.
Otherwise I would equip a wand that casts attack spells of the school of the wizard you're questing with, or if you're questing with more than one person pick a wand of the same school as the wizard you're trying to open holes for. If you're travelling with Storm, that's almost always an excellent choice.
When I meant the ice wands benefit fire wizards I heard it from Ravenwood radio and how they're useful for getting rid of shields for your convert build up. But I know balance doesn't work like that. At the moment my balance wizard is level 11.