Seriously, they just don't mix. When your child is wearing a bulky winter coat, you need to loosen the straps to get him buckled in. In the event of an accident, the force of the crash will cause the coat to compress, leaving empty space between the straps and the child - potentially causing baby to fly right out!
This video gives a great visual explanation:
But, but... it's negative 10 degrees where I live! How is my kid supposed to stay warm?!
Try using a thin fleece instead. Your kid won't freeze to death on the walk from the house to the car. Or, carry your child to the car in his coat, but take it off once you get him inside the car. Then buckle him in and put the coat on backwards, or use blankets.
It's a really simple step to potentially save your child's life.