What does the coop look like? Is it elevated or on the ground? What materials is it made of? What does your ventilation look like? How big is it and how many of what kind of chickens will you have? Is it protected or out in a wind? Do you have a thermal mass inside, like the ground?
There are two types of heat transfer, convection (air movement) and conduction (transfer through materials. Radiation is in this part too). Insulation affects conduction. In my opinion insulation is probably of more value in summer to keep heat from building up than in the winter to keep the cold out, but with some materials and locations/exposure of certain types of coops, it can help some in the winter. I’ve had chickens killed by heat. I’ve seen chickens sleep in trees in below zero Fahrenheit weather. I’m much more concerned about heat than cold.
A metal coop (or one made out of a thin conductive material) or an elevated coop can benefit more from insulation than a wooden coop on the ground as far as cold. Your concern is probably not the everyday weather you have but the cold snaps of extreme weather. The extremes are where you are likely to have problems.
I’m in a totally different climate than you, but I’d be more likely to build a good walk-in coop on the ground out of wood than to insulate. There are coops like that in Alaska that are not heated or insulated other than using building techniques and materials that provide natural insulation.