the physics is quite straight forward.. and Bluebee you are wrong... I assume you are just being provocative... in the vernacular of Northern England, this is a wind up. If the volume of bees to the surface area of the foam is high, then foam works very well. If the ratio is low, then the temp in the hive is going to track the average daily temp which is about 21F/-6C here right now. That’s what I call a freezer. What temperature is your freezer set to?
The few watts from a weak cluster of bees just get sucked up and absorbed by all that cold honey as opposed to warming up the hive. It’s a losing battle. In such hives the bees just keep moving slower and slower until the finally stop for good. :(
A freezer is an insulated cavity with a heat pump. I dont recognise any heat pumps in a winter colony.
Conventional hive geometry is very poor for higher temperature heat retention. It seems to assume that the air inside is a solid not a fluid.
Cold honey? where does this come from. The honey starts out warm, then heat flows hive resisted by its themal conductivity and delayed by its thermal mass.
If your surface area is too large for the heat source... Change it.
If you are getting mass transfer taking heat away .... Seal it.
Bees in tree nests have all of this solved. Like the ball catcher they have a good solution to the differential equations of the problem.
(p.s. they have feral bees in Alberta!)