Why not to use portable heater while driving

Maybe I'm missing something here: why was he running any heat, other than that from the cab's dash heating, in the first place? We've not done any cold weather camping in our MH yet, but in hot weather, we just run the cab AC, turn on the house AC only when we're parked. Wouldn't that work the same with the furnace, any heater? Run the cab heater on the road, turn on the furnace or space heater only when finally parked? What am I missing here????