Suicide doors were considered "suicide" to open or pop open on their own at speed.
As Vonparhkur mentioned about cars not having heaters; Many of the big sedans such as Packards, etc. had a rope like rack on the back of the front seat to hang a "lap robe' or "lap blanket".
We must remember that in the ealy days cars were not as dependable or able to travels as fast due to their mechanicals and also due to road conditions. Backroads, 2 lane highways were the norm. Consequently, the blanket in an early car had other uses too;
Roadside or meadow picnics were common. On a long journey through the country, you didn't drive through a burger joint; you brought a basket of food and drinks and took a break. IIRC, the Fords Forever book has a pic of a few farm Women having a roadside lunch next to their Ford.
Cars overheated and broke down more often. A break on a blanket or to lie on while working on the car.
Also, a guy might get lucky and get laid on, or under one, so it stayed in the car.