I was told in the hospital safety class to not put anything bulky under the straps. The reason is that under the forces of a crash, coat materials compress and result in the harness being on too loose.
I'm going with a wool onesie that's pretty thin and layers over footie pjs, socks under the footies, a pilot cap style hat, and eventually mittens (not cold enough yet), and a fluffy blanket on top.
For her stroller and carrier I got a wool romper with footies, a baby puff sweater, and a few wool shirts.
I figure in the car, the heater is going, and we avoid keeping her in the car seat outside of the car.