I would tie the snake up in a bag loosely and put that bag in a tub that will not allow for the snake to move around (aka out and over the tub edges).

I would not put it in an icechest covered. If anything, leave the top off. If you have to, yes, put holes in the top of the styroform, or every few hours open the chest to allow for airflow.

As long as the car is warm and comfortable to you, the snake should be fine until you get to your destination.