damp plywood on the underside of roofing?

More venting try for a while leaving trap door open see what effect you get. Most roof ply is/should be marine ply and can to a degree take moisture.
second Q;
No! the structure of the roof is constructed to take the weight of the covering plus estimated snow weight. If you have another roof put on this structure I've no doubt it would collapse if the weight was added to by snow, and even then with the added roof weight only it still may cause weakness in the rafters.
In other words 'You go down the cheap road expect problems'.

BB
February 2011