From what I've seen of the game so far, I don't think you really need a designated tank, but you may wish to be somewhat careful about your ability/gear mixes on each character.
This kind of boils down to the fact that the "holy trinity" (tank/DPS/heal) really isn't present in this game - there's no healer, in particular, and each class has DPS-style skills and tank-style skills. Although every hero is going to prioritize their primary stat, and some stats are better for defense than others, there's a wide variety of gear and skills for tanking available to everyone. Wizards aren't limited to low-defense "cloth armor" or anything.
Most of the classes can be spec'ed to be more or less "tanky" - for instance, I played several hours as a Witch Doctor with a Wizard, and we both survived extended periods on the front lines. With life steal items on my Witch Doctor, I can hit hard and hit often, and my health will bounce back as my mana drains. Then I can cast a crowd-control spell with mana recovery, and go back to pounding away with the DPS again. The Wizard was using a "diamond skin" spell that boosts defense, and would teleport out of combat if things are getting a bit too hot.
I would suggest that you each play whatever class you feel suits you best, and at least at the lower difficulties you can choose your abilities how you wish. When you start to get where the game is getting harder, you'll want to make sure that everyone can survive for at least a little while in a melee, and ensure that you're all properly balanced for survival.