I am in KY, East of you. The cold and heat seem more intense here because we always have humidity. "That cold KY rain" "AZ its a dry heat" Here in the summer at 85* I run into the AZ natives that beg to be home in triple digit temps.
I would Treat myself to a room. You may have to see if you can find a motel, church or shelter.
Mammoth Cave is great in the winter. The crowds are not as big and the underground temp is the same year round. It is a National Park well worth the trip.
This state is no place for a weather man. I have been hearing temps forecast as low as -6 But then back up to +50
I have a tarp over my boat for the winter. My boat is on a trailer. I have found the tarp will warm it up when I am out messing around in it. the tarp acts like an emergency blanket. At the extreme cold I do not know if you will have much help from a tarp. Maybe some one else can comment ?
Good Day, Lou