I moved my mother from Wisconsin to Dallas in December years ago and she wanted to take her houseplants. We made a small section in the back seat and stacked the the pots on each other and then secured them by putting boxes around them to keep them in place. I also covered them with a sheet to keep them warm. It was a two day trip.
We stopped at a motel overnight and couldn't take the plants in because of the way the car was packed. I decided to throw a blanket over them and tucked them in for the night. In the morning the car was freezing inside and I worried that the plants were going to die from the cold. I stuck my hand inside the blanket and it was warmer in there than the rest of the car. When the car warmed up I removed the top blanket. All the plants survived that freezing night. My tip is, if moving in very cold weather cover your plants while traveling in the car.