The frost was last year when I didn't have the drywall on the ceiling of the bathroom and didn't have the living room area of the upstairs ceiling sealed. This season I have both sealed and humidity is 30% also all electrical boxes on exterior walls are sealed with spray foam. All rim joists for the 2nd floor are spray foamed. Everything is pretty tight now and the humidity is still low. I wouldn't consider my house to be as tight as someone with all spray foamed walls and ceiling but I would think it should be pretty tight. I can't find any drafts with my IR thermometer around windows or doors.Just backing up to the original post, you say your house is relatively air tight, then say that one of the rooms in your house has no drywall on the ceiling and your attic is full of frost.
The issue here is that your house is really, really, really leaky. If you do a really good job of air ceiling your house - mean caulking electrical boxes to the drywall, caulking all the holes and where the electrical wire comes in, your humidity issues will go away.
A direct air source to the wood stove isn't going to do anything.