What a nice opportunity! These floors will look wonderful when you're done.
Well, other than the room being chilly you shouldn't run into humidity problems. I'm assuming the home is normally heated, right?
I just finished last coat of poly today on my floor refinish project (My Hardwood Floor Refinishing project
). I am so very pleased with the results!
I closed all the doors to bedrooms/baths and taped a plastic sheet over doorway to family room trying to keep the stink out of those rooms and prevent heat loss in those rooms as well. It was quite effective. I turned my heat off, opened windows and put fans in windows while I was applying the poly and 2-4 hours afterwards. So to answer your question - no you don't have to do that, but it will help.
If it were me, I'd use the orbital sander on ALL the floors. I don't think you need a drum sander unless you have real uneven floors, etc. I bet you'll be surprised at how great the orbital will work, even on the painted floors. You may have to use a few more sanding disks (36 grit) but I'm thinking it will work.
If you do the living room first using the orbital you could give it a spin on the painted floor to see if it will do the trick. If not, get the drum sander.
Me? I know my limitations and I could not handle the drum sander at this time... my body won't take that abuse. It about killed me 6 yrs ago and I'm not getting any younger!
Good luck on your project!