According to the TSA frozen water is allowed past so long as it is totally frozen and not slushy and has no water at the bottom of the container. Basically make sure it's really damn cold before you leave and hope it doesn't melt on you.
This is just a reminder that the rules are not intended to be followed or applied evenly. That's why none of the people who enforce the rules actually know any of the rules. The specific rules aren't really relevant to how the system functions. Instead, the concept of rules exists in such systems to justify the arbitrary exercise of power. You could literally show this to a TSA agent and probably half the time it wouldn't matter.
The whole thing was always theater with the bonus perk of getting folks used to fascism.
I’ve asked the TSA dudes while going through security this exact question and they confirmed that, yes you can take fully frozen water bottles through security.