In your climate, it may help. Purpose of insulation is to retain radiant heat generated by the birds within the coop. Result is it may boost inside temps by as much as 10 to 15 degrees over outside temps, which in addition to the temperature boost, helps move moisture out of the house. Danger from the cold is frostbite and that comes from cold damp conditions and frostbite of combs and waddles kicks in somewhere around 0F to +5F under the right conditions. So the need for insulation begins to kick in somewhere around USDA plant zone 6. Plant zone 5 areas and colder could probably benefit from insulation. Either that or raise cold tolerate birds with small combs and waddles.
BTW, moisture comes from the birds. Their breath, plus moisture in droppings accounts for 90% of it. That has to be vented, so tight houses are NOT want you want.
So it is insulation paired with a controlled level of ventilation to allow warmed, moisture laden air to move out to be replaced by cold dry air, which dries even more as it warms up. NO artificial heat. Heat source is radiant heat from the birds themselves, which is retained by the insulation.
BTW, if you do use insulation, use the hard foam board so rodents don't set up shop within a protected wall in the fiberglass stuff. Perfect setup for them. But birds peck at the hard foam stuff, so it has to be covered on the inside by hard surface like OSB, plywood, etc.