I'm still a newbie too, but I can tell you that the sundews (drosera) are deciduous. They will drop their leaves and they DO need to hibernate. I have mine sitting in the garage right now and I am just going out and adding enough water to keep the moss its in from compacting into a brick.
If you use distilled water, you will have to fertilize, so IMO, rain water is best. You can feed them two or three insects every three to six months instead of giving them fertilizer, but do not overfeed. Every time they close their leaves around an insect to digest it, it causes leaf damage. They can close around an insect just a few times before the plant will drop the leaf, so be careful about providing nutrients for them this way.
If you figure out some magical method for getting yours to thrive in that tiny set up of yours, please share! I have a butterwort too and it's doing ok, but I would love it if the little guy could thrive.

---------- Post added at 02:47 PM ---------- Previous post was at 02:46 PM ----------
Also, where did the glass case come from? I'd love to do something similar with my carnivorous plants! That's pretty swanky looking!