Forget about the space heater in an enclosed area, could depend on type though. When you get to Willis, if at Sunset Shores, ask about the rig that just burned to the ground 2 days ago from doing just that.
No one was injured, they all got out.
The biggest problem at the 2 Willis parks is the hose bibs aren't well insulated and they will freeze. So drip the faucets as needed.
John
2021 Airstream