uhhh, your furnace runs on propane, not 110v AC electricity.
the furnace fan and electronics are 12v battery powered.
unless you're talking about taking a space heater. and most campgrounds don't allow generators running at night.
all your Honda will do is recharge the batteries, after the furnace depletes them from running the propane furnace all night.
and Zoe the Wonder Dog(R.I.P.)
'07 Roo 23SS pushing an '07 Chevy Avalanche
Equalizer WDH and Prodigy BC