I use a double bucket system that I made. The outside bucket is the larger in diameter and depth. The second bucket is shallower, sits nicely inside the slightly larger one and easily lifts out. I drilled small holes around the bottom side of the smaller bucket, leaving an inch of space or so up from the bottom for the holes.
This makes changing water easy. If the water is changed periodically the water will stay unfrozen and it will replenish the oxygen. Just pick up the inside bucket and all but one inch of water drains out. Dump out and refill the largest bucket and reset the drained bucket inside. In times when I have forgotten my little minnow net, I have lifted the interior bucket to let the water drain and just picked out the minnow of choice. I do not do this too often, as I think it may stress the minnows some.
For refilling the bottom bucket I cut the top "corner" off a windshield washer fluid plastic jug, leaving the handle attached to the bottom. This fits down a hole and pushed down, will fill with water. When it is not in use for refilling, I keep a little water in it with a couple of minnows so I can easily carry them from tipup to tipup when checking my line or when there is a flag and a new minnow is needed.
Best of all was the cost, in $ = 0.00, time = half an hour to make, the time on the ice, priceless . . .
I have not added any Styrofoam inside the buckets, but have thought about it to soften the sides of the bucket for the minnows.
-Reelcharacter