Frozen food can be brought in your carry on luggage onto the airplane as long as the frozen food is completely frozen when you go through the airport security.
The ice packs must also be completely frozen to be allowed onto the plane through your carry on luggage.
Frozen food, frozen water and other frozen liquids can be brought onto the plane through carry on luggage or in your checked luggage.
You just have to make sure the food or liquids are frozen and not melting when you bring the frozen foods or liquids through airport security.
I've brought frozen food, frozen water etc onto the plane through airport security and it has always been allowed.
I've carried it on carry on luggage and everything went just fine.