The condensation freezes because the wall of the freezer will dip below 32 degrees during a cooling cycle. If the freezer wall never got below your 40 degree setpoint it would take quite a while to cool anything.
There are a lot of threads on the topic of condensation. Make sure you don't have any air leaks, and that every seam is caulked. And stop opening the damn thing! At that point you've done everything you can, and you should still expect some condensation.
As day_trippr pointed out in another thread, during a cooling cycle the pressure will drop in the freezer so it will pull some outside air in. So condensation is inevitable.
The desiccants work pretty well as long as you have air movement in your fridge. I have an eva-dry that I have on the compressor hump right below where my fan is mounted; that's generally enough to prevent condensation, and I only have to regenerate it every 5 weeks or so. Others have had better luck by mounting fans directly onto the desiccant.