We have the cords you are referring to in all of our vehicles thought most of Alaska.
Placing any toaster under the oil pan could be dangerous, but some of us did things like that in the past. I did all kinds of crazy things when I was young, and have no idea how I made it though such events without hurting others or killing myself, including walking on the ledges of two store building to showoff and impress my friends. My teacher chewed me up to nearly death
Before engine heaters, some Alaska bush pilots had to place a metallic pan loaded with lit charcoal to warm the motor before starting it. I don't know the details, but I assume that they had to place a metallic mesh to prevent flames to rise. Other pilots would drain the warm oil from the motor, bring it indoors and close to the wood stove to keep warm, and then before starting the motor they would refill the motor with the now hot oil before starting it.
Most people leave their cars and trucks running are the shopping centers' parking lots whenever the temperature drops to perhaps -10 or colder 6temperatures. The reasons for this is that if one is buying...lest say lettuce, flowers, and things like that, they would freeze between before one can open the car's door and bring it inside the warm cabin. My wife has insulated bags she uses to keep the veggies from freezing, but these things are bulky. Anyway, just like my wife and I, most people start their vehicles using remotes and leave the motors running at the supermarket parking lots. These starters systems incorporate safety modes to prevent thieves from stealing the vehicle while the motor is running.