Ah, but there IS heat being generated in the coop, by chickens and by
sunlight. Also there is the natural warming of the air during daytime.
The better you can capture that heat and make it last through the night, the warmer (well, "less cold") your coop stays.
Insulation DOES NOT, in my experience, decrease heat gain during winter, because your walls were not transmitting any meaningful amount of heat anyhow, and your roof HAS to be at least a little insulated in cold-winter climates just to avoid it becoming a ventilation-defeating 'condensation farm'. Your wintertime heat gain from the environment, during the daytime, is almost totally from sunlight coming in through windows; and to a much smaller extent the warmer (i.e. not as cold as nighttime) air coming in your vents. Sun coming through your windows DOES generally warm a well-designed coop up quite noticeably during the day, especially with well-insulated walls. THis is not theory, this is what actually HAPPENS.
I do not heat my coop, or my barn either, but they benefit QUITE GREATLY from their fairly thick insulation. Again, not theory, OBSERVATION
Whether to insulate a coop in Connecticut is personal choice - well-chosen healthy chickens will not necessarily *need* an insulated coop in that climate, but it will make them more comfortable and it will make your coop management easier. So it is still a good idea to do, if you feel like doing it. And if you are even remotely contemplating running electric heat -- even just to keep water thawed -- it becomes even more of a good idea, because the warmer the coop stays b/c of insulation, the fewer watts you need to use.
GOod luck, have fun,
Pat