Can my cactus (small) be planted in a fish bowl with perite and sand mixed with some soil?

I'm moving from Utah to Minnesota and need my cactus to stay inside during the winters there. I was thinking of making a cactus aquarium where I set up a fish bowl with a couple small cactus. My plants were to put perlite rocks on the ground level of the bowl, than follow with my sand and dirt mix, and top with more perite when I plant the cactus in there. It won't need much water in the winter at all. But, will it survive in this kind of environment?