There are pros, and cons on insulating.  There are also different insulating materials used.  Without pictures of coop, ventilation present,  and details on insulation used, I would have to write a small pamphlet to cover all situations. 
Provide some pix and details, and you will receive comments. 
No idea what a little tack room is.   Is it a tackle room for storage, or a small attached room for whatever.??? 
WISHING YOU BEST,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, 
