Is it important to use special fasteners in treated wood for non-structural applications?
The hot-dipped galvanized requirement isn't for load, it's to prevent corrosion.  For less load, you can get smaller nails.  However, if you don't use the hot-dipped galvanized, then the chemicals in the PT lumber will cause a reaction with the metals in the nails and they will corrode much faster than if the nail was installed in non-PT lumber.  Here's some more info:

http://www.strongtie.com/productuse/PTWoodFAQs.html