Finding another frame is not a bad idea - winter can absolutely ruin a bike. Also, cheap bikes have thicker walled steel tubing (takes longer to rust through) and usually horizontal dropouts so make ideal winter conversions.

However, your 12 Y.O. giant is not a museum peice and an old rear derailleur makes an excellent and inexpensive chain tensioner - I prefer 70s and early 80s Suntour derailleurs as they are cheap, plentiful, and look good.
Put some type of rust inhibitor inside the frame tubes and build 'er up! You have 6 months before the snow starts to fall.