i thought that the connections that create memories began decomposing as soon as it ran out of oxygen
If you were to preserve a brain, but remove all electrical impulses for while, then turn it back on, it would still be the same person with the same memories and personality. That is exactly how cryogenic freezing would work, if we could successfully thaw the person out. If you were to be cryogenically frozen for 1000 years, to you it would seem like you just took a short nap.