I would never leave my TT in the Dallas TX area for a week in winter without doing a basic winterization. What we would get is nothing like what you would get up there.
As full-timers, I still carry RV anti-freeze and can do a basic winterization if needed. Which I have had to do when power went out due to an ice storm in west Texas with temps falling into the low teens.
I've had to disconnect my fresh water and sewer lines due to freezing temps in Florida.
If you are where the temps will drop a bit below freezing for a few hours at night but warm up above freezing during the day a well insulated rig will be fine even without power.