You could do what I did for my helmet. I took two battery packs that hold 4 AAA batteries and hooked them up in series so that the 8 AAA batteries (@ 1.5v each) would produce the 12 volts.
I thought about that but I'd prefer not to put that much weight in my helmet. Space could also rule that out. The nice thing about doing it that way is I would just wire my LEDS into that supply with the proper resistors and a second slide switch (so lights and fan are independent) so that keeps it on the table.
Reventant, the 12V battery you are thinking of is an A23 type. Is basically some button cell batteries stacked together in a casing. Not very useful for running a fan.
Wiki gives it a lifespan of 55mAh, lame. By comparison, a 9V battery has a lifespan of 560mAh and AAA are 1200mAh.
http://en.wikipedia.org/wiki/List_of_battery_sizes
If you want the BEST weight to power ratio, can pick up a lithium rechargeable pack from here. You will need a few in series to reach 12 volts. Lithium does have a tendency to burst into flames when used improperly, so... watch out for that.
https://www.sparkfun.com/products/9876
Edit,
Here is a ~12V battery lithium ready to go. Just add a compatible charger and wire harness connector for your helmet. Weighs 6 ounces.
http://www.hobbypeople.net/index.php/hobby-people-11-1v-2200mah-20c-lipo-battery-pack-w-t-conn.html
I had this crazy idea... speaking of arduinos again...could it be possible to wirelessly switch on all the lights in my suit with an arduino?
well I was thinking, how long would it take to manually turn on each and every light? that would be a butthurt, in contrast to how cool would it be to press a button on the cheek inside of your helm and turn all of your lights on at (relatively) the same time? awe-inspiring to the rubies fanatics. 8)