In my research, I have read that chickens do well without insulation depending on coop design.
Birds take shelter in trees or under bramble in the wild and have very few protections from weather.
Choosing chickens for their hardiness, such as very cold hardy, can help improve your success in cold winter weather.
Metal is a good conductor for temperature so I would assume that it may help keep the air within the coop colder than their wood clapboard counter parts so I understand your concern.
How large is the coop? Do you have dimensions?
Do you have wood studs or all metal construction?
What material is the floor made of? How is the floor constructed?
What state or part of the country do you live in?