TTs aren't particularly well insulated and have air leakage. That heater could end up running non-stop, even on the lowest setting. I don't think it's safe to have that type of heater running 24/7 all winter. You can also expect a higher power bill too.
I installed a permanently mounted recessed 1000 watt heater in a previous 20' TT and even with the t'stat set as low as it could possibly go, it ran continuously because of the high heat loss. I wanted to keep it warm because I was doing a lot of interior mods, but after our power bill went waaay up, I shut it off.
It's standard practice to winterize and leave unheated. Many also leave it plugged in to keep the battery charged.
Having said that, I read a lot of reports of sheet flooring cracking due to the extreme low and extended temps. of the past winter. Don't know what precautions that can be taken that's safe, other than maybe rigging up a few 120V incandescent bulbs sitting on raised bases to raise the interior a few degrees when it gets really cold out?