Insulation problem

I have a house that was built in the early 70s in a cool climate. The house has an overhanging roofline and the rooms in the overhang are always cold in the winter and extremely warm in the summer. I openned the soffit and took a look at the insulation and it appears that it is only batting between the studs with nothing else covering it. So drywall, batting and then the space between the roof. Bad design but now I need to fix it somehow.
So my question is: if I were to shove pink solid sheets up and glue them to the studs, would there be any issue of condensation in the winters? As far as I can tell there is no vapour barrier against the drywall and the drywall itself is the old style made from mostly carboard with a bit of cement. Im debating removing the drywall and trying to do something from the inside but since there is nothing behind the studs, im not sure what would be possible.

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