i've been on 5 RV forums for over 5 years and i've never heard of anyone running the furnace in their trailer while driving!
i have heard of motorhomes running the chassis' heater but that would be in any vehicle with an engine.
IMHO, it doesn't take that long to heat up if you really need it warm fast. i would never drive with the furnace going in my trailer.
when you pull into the campsite, start the furnace then and it'll be warm by the time you level, put the stabs out, unroll the awning and unhook the trailer.
and Zoe the Wonder Dog(R.I.P.)
2016 PrimeTime TracerAIR 255, pushing an '07 Chevy Avalanche
Equalizer WDH and Prodigy BC