I SWEAR by my Frabill four seasons two-piece live bait bucket!! I took a picture of it but can't figure out how to append it to this message. Maybe someone can tell me how to do it...
Anyway, the inner bucket - which has a lid and contains the bait - fits into the larger outer bucket. The water that sits between the walls of the inner and outer buckets freezes solid and insulates the water within the inner bucket. I've never had the inner bucket water freeze over completely, no matter how bitterly cold it got outside. The whole thing is also small enough to fit snugly between all the other stuff on my ice fishing sled. In addition, I like to refresh the bait water when I get to a pond in the morning. It's easy: drill a hole through the ice, lift the inner bucket up and simply plunk it inside the hole to change the water!
Finally, and as a bonus, I use my trusted bait bucket in the spring when I troll for salmon or trout with live bait. Because of the two-piece system, it's easy to lift up the inner bucket and drop it in the pond to refresh the water when needed.
WalMart sells them for $10-15. Best investment you'll ever make for a bait bucket.