Should I install a solar panel on the roof?

I'd do your homework to find out how much things cost, but with a 37 foot rig, there should be plenty of space for panels and a decent charge controller. With a few panels, you can easily get enough watts to offset the furnace's drain in the wintertime.

This won't run the A/C or microwave, but it will help with keeping batteries topped off, regardless of access to power.