As you already know, you won't be able to keep the area under the hoop above freezing [for a greenhouse of that size, single glazing, your climate, etc]. If you could, then you'd be the hero greenhouse guy for the northern part of the US.
Water barrels will definitely hold some heat but they will probably freeze. If you can keep the barrels from splitting open, you may be onto something though. The phase change from liquid to solid takes a ton of energy. So as the water freezes it holds the temperature around it at 32F for a long time. Then when it melts, it absorbs heat for a long time keeping the temp down at 32 until it's done. Whenever the day to night swings align with the tank freezing and thawing, it would do a lot to keep the temps around 32. So maybe in Dec and Jan you'd have frozen thermal mass, but for Nov and Feb they'd start phase changing most days to help keep you at 32.
Anti freeze would keep them from splitting so you'd have split free thermal mass. But since they wouldn't be freezing you wouldn't get the phase change advantage.
Just a few thoughts, probably a bit off topic from where you were headed
Dumb question, but if the temperature swings under the hoop don't affect the coop much, why do you care about them? The chickens aren't out at night so they won't mind that it's cold out there. I don't have chickens yet so I may be missing something...