One strategy would be to incorporate the attic into the conditioned space and then use a sandwich of barriers and insulation under a furred vented over roof to control ice damming.
Insulating a manserd roof.
One of the best ways to protect your mansard roof from the problems of ventilation is to use a vapor barrier on the.
If you are insulating with air permeable insulation material something like cellulose on the attic floor then my recommendation is to vent the attic.
One possible improvement could be a 45 soffit on the inside to provide both better insulation and venting to the upper zone.
Assuming that the attic you describe has a low slope roof you should follow the advice in this article.
If you have an existing house with this style then dense pack cellulose or pour in place open.
Metal exterior shingles and metal gutters result in a long roof.
Step 3 add foam insulation.
Insulating mansard and gambrel roofs new construction.
Hitting amazing levels of 0 13w m will need 300mm of mineral wool or 180mm of rigid foam.
Insulating a mansard roof.
Step 1 add a vapor barrier.
Through insulating during a conversion to a mansard roof you can lower your heating regularly and enjoy extra usable space through the house extension.
Insulating low slope residential roofs.
Step 2 add caulking.
An option on a mansard style roof would be a cupola on top for venting.
As always with ice dams air sealing and insulation are the first concerns.
Achieving a u value of 0 20w m meaning your roof will be better insulated than your walls will need 120mm thickness of rigid foam or 200mm of mineral wool or natural insulation.
This works everywhere no matter what kind of roof you have what kind of attic you have or where you live.
During the process framing you can incorporate the details of installation into the style of roof for quality heat savings.