Overwinter them in the fridge.

I have all my plants in a bog outside, when it goes below 0 degrees F.most of the pitchers are killed anyway leaving only the rhizomes to come back in spring and they do just fine. They do need to be kept moist throughout the winter though.

I've also seen S. purpurea frozen solid in the ice in the boundary waters of Minnesota so they may well be able to stand your balcony for the winter too!

No, I know for a fact that they won't survive the winter on my balcony. They won't even survive in the ground here. Zone 3 is just beyond their hardiness. But I can handle a bunch of rhizomes in my fridge. Should I keep them in plastic bags, so that they stay moist? Won't they rot?

Barely moist in ziplock bags with spagnum should do the trick!

For the record, if you're talking about the native Sarracenia species (purpurea?), it is indeed hardy below zone 3. You'll see it in bogs in the boreal forest...of course, the problem is getting out into the center of a bog to look, LOL! It's easy at a place like Boundary Bog Trail in Prince Albert National Park, Saskatchewan, where the floating boardwalk gets you right out there with the pitcher plants, sundews, bog rosemary and the odd loon...wonderful! Of course, hardiness depends on getting seeds or plants from hardy stock, too, rather than from more southerly populations.
We got S. purpurea (and some other species or hybrids, haven't researched them yet) last year and are trying it both in an outdoor acid bed, and wintering it in a coldroom (along with the other species/hybrids).