We've pulled our 5er to Florida twice. It was darn cold inside the trailer (unlike a motorhome that at least receives dashboard heat) - but once parked, the furnace heated it up rather fast. In OUR case, we couldn't run the furnace while traveling even if we wanted to (we didn't) because our closed slideout covered 2 of the 4 heat registers, and it's not good for the furnace fan to have blocked vents.
*IF* we had cats, I would have carried them in a crate in the back of our truck, where it was warm and reasonably quiet. I don't know how noisy a 5er is going down the road, but I suspect it creaks, rattles, and suffers from wind noise.