See if you can get a good sleeping bag, like one with a hood on it, and maybe even if a small personal thermal tent if you can fit it in your car.

This Life Tent is $20 bucks on Amazon.

https://www.amazon.com/Go-Time-Gear-Emergency-Survival/dp/B07NVWY95Y/ref=sr\_1\_20?keywords=personal%2Bcold%2Bweather%2Btent&qid=1637524659&sr=8-20&th=1