Frozen items are allowed as long as they are frozen solid when presented for screening. If frozen items are partially melted, slushy, or have any liquid at the bottom of the container, they must meet 3-1-1 requirements.
Though it is under special needs. Also no sure how you are going to keep it solid all the way through security. Particularly if you have a long drive to the airport.
I wouldn't bother - the chances of it melting are pretty great and personaly the less attention I bring to myself and my family at security the better.
Depending on what you want to accomplish there may be better ways. Want water for the flight, bring an empty water bottle and fill it at the fountain after security.
Need to keep food cold, use frozen grapes, etc.
If you are not traveling with medicines that need to be kept cold or a baby/toddler I am not even sure that exception applies.