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Did the water actually freeze? I think cold temperatures just slow them down or make them inactive but doesn't actually kill them. Throw some ammonia in and test it out to see if it gets processed at all.
I think from memory it goes dormant. I remember a discussion on this but away from desktop. I think it was when everything warmed back up again that there may be trouble as everything is sluggish to get re-started. Another one for JLK.
I would add some ammonia and see what happens next. So far as I know, it takes more than we think to kill off BB entirely. They're not as fragile as many claim they are. But it might take a short time to completely reboot the cycle, as the numbers of BB may be fewer than before.
I don't think you cycled for nothing, for sure.