I never tried freezing mine, and I don't really have much to say about that. Since you are in Canada, its possible the booklice may be able to withstand colder conditions, especially if they are something native to the area and not just brought in from somewhere warmer. I also don't really know how the ants would feel about being put in the freezer, which is why I didn't try it with any of mine (though all mine are warmer climate species). Still, I don't think very many, if any, ants like being in a freezer for long periods. Even acorn ants die a lot, if they are too close to the surface or not insulated enough and they are found in really cold places.
Maybe someone else will have feedback on the subject about freezing ants for a short time.
Though, I probably would move the ant colony infected with booklice somewhere else and anything else they have gotten into. And clean the area with soap+water+a sponge. The booklice (the ones I had) get EVERYWHERE. With that said, once you remove the source they are from (so my one formicarium, plus the oat container), they disappear really quick and its not that hard to clean them up after that. Mine never actually bred inside any of the clothes or storage containers, they were just exploring for new food sources. So, once I got rid of them inside the formicarium and cleaned up most of them on the walls, they disappeared pretty quick after that. The problem is, whatever they are breeding in (food container, ant farm etc), they just breed so fast, hence why it took an entire month to clean them up. Luckily they are harmless to ants, but I don't have any other "pet" inside the closet.