Your mind would still exist even when cut off from all inputs.
Practically, cryonics is currently just fancy death in a steel coffin filled with liquid nitrogen; but if it wasn't death, if it was actually reversable, then your brain literally frozen is conceptually not that different from an AI* whose state is written to a hard drive and not updated by continuous exposure to more input tokens.
* in the general sense, at least — most AI as they currently exist don't get weights updated live, and even those that do, the connectome doesn't behave quite like ours
We don't yet have useful words for what it is.
If the contexts are never deleted, it's like being able to clone a cryonics patient, asking a question, then putting the clone back on ice.
Even if the contexts are deleted but the original weights remain, is that murder, or amnesia?