Get the furnace working, blow hot air, do nothing exterior from December until March unless its a dry day. 

If it's kept dry, it's fine.

But once that well dries out, these Landlords will be ready to throw them out.

If on the other hand, they don't even come close to passing your screening then cut and dry would probably be the best option.

The owner of the unit above me has been extremely uncommunicative - she was pretty averse to any sort of mitigation action as her HO-6 adjuster told her as long as she dried up the water herself she was "all set", despite my telling her that her subfloor was obviously waterlogged and moldy.

Her being uncooperative is big trouble and she needs to understand you are serious.

Tiffany was lying nude on her bed under a sheet in the back bedroom.

There was crazy headwinds in 2007 and cash was dried up.

Is it towards colder climates, warmer, moist or dry?

It was also raining pretty hard while I was there and it was dry so it's most likely not from the side of the house and the roof would be a long shot to flow around the floor above it and just end up there.