Best to wait for sun and see what happens before thinking too much.
In the sumer with sun your 120 watts should be plenty to keep things topped off. It all just depends, but for light use you are good.
In winter when days are short, the sun low and many cloudy days then at best the panels will be good for keeping batts topped off for storage (not for daily use). But it all depends.
You said "folding" so this is a portable system...
How long is the wire going from panel to the battery?
How heavy a gauge is the wire?
Where is the controller located in that wire (close to panel or close to batt)?
I assume with folding/portable that you are pointing it to the sun, correct?
Yes, the furnace fan is a power hog. If it is a cold night and with good batts that might be all you want to power up after about 3 pm in the afternoon. Good idea to change habits. some ppl heat the cabin when they are up and about in the evening, then turn off furnace and just get under the blanket, then turn it back on right before the alarm goes off.