A friend of mine posted a link to an article and video that discussed something that I had been thinking about. My son has a big puffy ski-like winter coat and it was really difficult to strap him into his car seat while wearing it and I thought to myself, maybe he'd be better off without it on... turns out my instinct was correct!
The following video Winter Coats & Car Seats Don't Mix describes the problem with these big puffy winter coats. Basically if you put your child in a coat and strapped them into their car seat and tightened the straps, they would seem snug in there. WRONG! If you then unstrap them without loosening, remove the coat, and put your child back in there you will find there is a ton of extra slack in the straps.
The problem is with the compression of the winter coat in the event of an accident. The coat will compress in the event of an accident and it will be like you barely strapped your kid into the seat as demonstrated in the video above. The short of it: Dress your baby in warm clothing, bring a blanket to tuck them in after being strapped, and keep a coat with you in the car to put on them when you get to your destination.
You can read more about coat compression here on carseats.org: Padded inserts, blankets, and bulky clothing