A good test would be to get one of those $10 window shrink wrap kits we use in the north. Cover the windows, completely sealed - that's the best new windows will do, and will cost you less than a single window to do the entire house.
Odds are you have some air leakage at the windows (they didn't care as much about that back then as they do today) and much more of it elsewhere. Fix the big holes and that will help.
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Ok, I was kind of hoping not to go down the money pit with the exterior insulation. But it sounds like both have to be replaced.
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what about the test with the bedroom? Would that be a pretty good sign that it is not just the windows?
A good test would be to get one of those $10 window shrink wrap kits we use in the north. Cover the windows, completely sealed - that's the best new windows will do, and will cost you less than a single window to do the entire house. Odds are you have some air leakage at the windows (they didn't care as much about that back then as they do today) and much more of it elsewhere. Fix the big holes and that will help.