An attic or an attachd garage or the fridge would be a better solution.

Hey!
I have found that my dorm-fridge or a drafty windowsill work fine at forcing carnivorous plants into dormancy. This has worked for me with both my VFT and sundew. If you try this ice cube method, please let us know how it goes!

Here is a link that might be useful: Envi Sci and Fishy Plants

Crushed ice does not really induce this dormancy as is the effectiveness in growing high elevation cool growing species. You just need to bring the entire root and atmospheric growing temperatures down gradually and slowly adjust their growth to adapt to this cooler to colder extremes.
Shocking it with ice can also kill the plant not used to freezing temperatures from warm to frozen.