Don't believe me?
Okay if you insist, lets have a play.
* Put your child's coat on as usual.
* Place them in their carseat and fasten the harness, adjusting and tightening it until you can no longer grab or pinch any of it between finger and forefinger.
* Undo the harness without adjusting it.
* Remove your child's coat and refasten the harness, again without adjusting it.
* Is the harness now loose? Can you pinch the belt, gathering it? If so your baby/toddlers coat is too bulky to be worn under the harness. The harness would be too loose to be effective in the event of a crash, the harness is essentially protecting your child's coat and not your child. In order to offer effective protection, the harness needs to be flat against your child's torso.
Try putting the coat on back to front after they're fastened into the harness so it acts as a blanket or else use a blanket some of which can be fastened to the car-seat. You can even buy the equivalent of a buggy snuggle for a car-seat. Even a fleece sleepsuit or onesie (not snowsuit) could help as they're thin yet warm.
A quick search on YouTube showed me a video by a user called tcooper81 which perfectly illustrates what i'm waffling on about, so watch and be safe. I've included this video with their kind permission.